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UBC Theses and Dissertations

Subjective evaluation and comparison of digital and analog modulation systems Douville, Rene 1968

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SUBJECTIVE EVALUATION AND COMPARISON OP DIGITAL AND ANALOG MODULATION SYSTEMS by RENE7 DOUVILLE B.A.Sc, University of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULEILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard Research Supervisor Members of Committee Head of Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA September, 1968 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of f~CT/f/cXL The University of Brit ish Columbia Vancouver 8, Canada Date ABSTRACT The ultimate measure of performance of any communication system i s the subjective quality of the received message. In th i s thesis, the subjective quality of the output of a d i f f e r e n t i a l pulse code modulation (DPCM) system was measured as a function of the number of b i t s of quantization L, the speech bandwidth W, the r a t i o r of the sampling frequency f to the Nyquist frequency 2W, and the number of s feedback samples N. For previous-sample feedback (N = l ) the maximum subjective quality was obtained as a function of the b i t rate R = 2rWL. The optimum sampling rate .was found to be the Nyquist rate; the im-provement afforded by increasing f over 2W was more than offset by the required increase i n b i t rate. Noise i n the feedback loop caused by dc offset errors and noise present i n the output of the feedback coeffi c i e n t amplifiers prevented a thorough investigation of two- and three- sample feedback, although some results were obtained. The subjective quality of delta modulated (AM) speech was obtained vs r and W, and the quality of amplitude modulated (AM) speech was measured as a function of W and channel signal-to-noise r a t i o . A technique was then devised to use the AM results to estimate the sub-jective quality of phase modulated (PM) speech. A comparison was then made of the c a p a b i l i t i e s of PCM, DPCM, AM, single sideband-AM (SSB-AM), double sideband-AM (DSB-AM), andPM. It was found that when the available channel capacity i s small, SSB-AM and DSB-AM are subjectively better than PCM', DPCM, and AM. However, for high quality speech communication, DPCM requires less channel capacity than PCM, AM, DSB-AM, SSB-AM or PM. TABLE OF CONTENTS . Page ABSTRACT... i i TABLE OF CONTENTS i i i LIST OF ILLUSTRATIONS ' • v LIST OF TABLES v i i i ACKNOWLEDGEMENT i x 1. INTRODUCTION 1 1 .1 Communication Systems 1 1 .2 Brief Review of Source Encoding Techniques 2 1 .3 Scope of the Thesis 5 2. SIGNAL-TO-NOISE RATIO IN PCM, DPCM, AM, FM AND PM 7 2 . 1 Signal-to-Noise Ratio i n DPCM 7 2 . 2 The Effect of Sampling at Higher than the Nyquist Rate 11 2 . 3 Signal-to-Noise Ratio i n AM Communication 13 2 . 4 Signal-to-Noise Ratio i n Angle Modulation 15 3 . REAL TIME DPCM AND AM SYSTEMS... 20 3 . 1 A Real Time DPCM System 20 3 . 2 Disadvantages of the System Used 22 3 . 3 Measurement of AM Signal-to-Noise Ratio 24 4 . SUBJECTIVE TEST PROCEDURE 27 4 . 1 Introduction 27 4 . 2 Preparation of Speech Samples 29 4 . 2 . 1 DPCM Samples 29 * 4 . 2 . 2 AM Samples 31 4 . 3 Paired Comparison Tests for Determining Isoprefer-ence Contours 31 4 . 4 4 - 4 . 1 Paired Comparison Tests 31 4 . 4 . 2 The. Method of Paired Comparisons 32 4.3-3 Selection of Test Points and Derivation of Isopref erence Contours.. 35 4.4 Scaling of Isopref erence Contours... 37 4.5 T r a n s i t i v i t y Checks 38 5. RESULTS, EVALUATION AND CONCLUSIONS 40 5.1 Results of the DPCM Subjective Tests 40 5.1.1 Determination of the DPCM Isopreference Surfaces 40 5.1.2 Discussion of DPCM Curves and Surfaces..... 46 5.1.3 Minimum Bit Rate Loci 53 5.2 Results of the AM Subjective Tests.. 60 5.2.1 AM Results and Discussion 60 5.2.2 Extension of AM Results to Angle Modulation 60 5-3 Comparison of PCM, DPCM, AM, DSB-SC, SSB-SC and PM 63 5.4 T r a n s i t i v i t y Checks 69 5.5 Concluding Remarks 70 APPENDIX 1 71 APPENDIX I I 75 REFERENCES 78 LIST OF ILLUSTRATIONS Figure Page 1.1 A general communication system 1 1 .2 A general d i f f e r e n t i a l pulse code modulation (DPCM) system 3 2 . 1 A p r a c t i c a l DPCM system 8 2 . 2 (a) Spectrum of quantization noise, (b) Quantizing noise a l i a s i n g due to sampling, (c) Output quanti-zation noise. Note that increasing f decreases the contributions due to a l i a s i n g 12 2 . 3 (a) A double sideband suppressed-carrier amplitude modulation system, (b) Ideal lowpass f i l t e r charac-t e r i s t i c , (c) Assumed power spectrum of the base-band input signal 13 2 . 4 (a) Angle modulation systems, (b) Characteristics of the ideal RF ( H R p ) , IF (H I F) and lowpass (E^) f i l t e r s 15 3 . 1 A system equivalent to Figure 2 . 1 when channel noise i s neglected 20 3-2 An implementation of Figure 3 ' 1 £or N = 3 21 3 . 3 An integrator network 23 3 . 4 A system whose output i s equivalent to the DSB-SC system i n Figure 2 . 3(a) for A = 1 24 3 . 5 C i r c u i t for measurement of mean square power 25 4 . 1 Power density spectra of speech 28 4 . 2 Autocorrelation functions of lowpass f i l t e r e d speech versus the sampling period l / f 30 4 . 3 An isopreference curve. Points b ^ ( i = l , — 4 ) are compared to point A and the results of the compar-• isons used to determine point B 33 4 . 4 (a) A psychometric curve corresponding to the d e r i -vation of point B i n Figure 4 . 3 - (b) The curve of (a) with the ordinate i n unit normal deviates 34 4 . 5 Five planes passing through a reference point (P)..' 36 5 . 1 Isopreference contours i n L = constant planes (L i s the number of b i t s of quantization). The scale value s and standard deviation cr associated with each contour i s shown next to the reference point through which that contour passes 41 5 . 2 Isopreference contours i n W = constant planes (W i s the bandwidth). The scale value s and stan- . dard deviation cr associated with each contour i s . shown next to the reference point (drawn solid) •through which that contour passes 42 5.3 Isopreference contours i n r = constant planes (r i s the r a t i o of the sampling frequency f s to the Nyquist rate 2W). The scale value s and stan-dard deviation & associated with each contour i s shown next to the reference point (drawn solid) through which that contour passes 43 5 - 4 Isopreference contours i n planes defined by equa-tions of the form r = kW. The scale value s and standard deviation cr associated with each contour i s shown next to the reference point (drawn solid) through which that contour passes 44 5 - 5 Isopreference contours i n planes defined by equa-tions of the form r = mW + b. The scale value s and standard deviation o* associated with each con-tour are shown next to the reference point (drawn solid) through which that contour passes 45 5 . 6 Pinal isopreference contours and contours of con-stant b i t rate i n the r = 1 . 1 plane. The scale value s or b i t rate R associated with each contour i s shown on the contour 47 5 . 7 Pinal isopreference contours and contours of con-stant b i t rate i n the r = 1 . 3 7 5 plane. The scale • value s or b i t rate R associated with each con-tour i s shown on the contour.... 48. 5 . 8 F i n a l isopreference contours and contours of con-stant b i t rate i n the r = 1 . 6 5 plane. The scale value s or b i t rate R associated with each con-tour i s shown on the contour 49 5 . 9 F i n a l isopreference contours and contours of con-stant b i t rate- i n the r = 2 . 5 plane. The scale value s or b i t rate R associated with each con-tour i s shown on the contour 50 5 . 1 0 F i n a l isopreference contours i n the L = 4 plane. The scale value s associated with each contour' i s shown on the contour 51 5.11 Pi n a l isopreference contours i n the W = 2.12 KHz plane. The scale value s associated with each con-tour i s shown on the contour 51 5 .12 An isopreference surface. Contours of constant L , W and r are shown 52 5 .13 The va r i a t i o n vs r i n the parameters a(r) and b(r) i n the equation W = a ( r ) 2 b t r ) L 54 5.14 The scale values corresponding to the intersection points of W = a( r ) 2 k ( r ' l ' with isopref erence con-tours i n planes of constant r as functions of (a) the required quantization b i t s (b) the required bandwidth 55 5.15 The maximum attainable scale value for a fixed b i t rate R plotted for various values of r. Also shown are results presented by Donaldson and Chan for DPCM (r=l.l) and PCM. The points marked by X cor-respond to maximum scale values for AM 57 5.16 Curves of scale value versus (a) bandwidth W (b) r a t i o of sampling frequency to Nyquist f r e -quency for the special case of L = 1 . Also shown are contours of constant b i t rate... 58 5.17 AM isopreference contours. The scale value and standard deviation associated with each contour i s shown next to the reference point (drawn solid) through which that contour passes. Also shown are contours of constant channel capacity for DSB-SC (C-p) and SSB-SC (Cg) communications systems 61 5.18 Phase modulation (PM) isopreference contours and contours of constant channel capacity for the peak frequency deviation | A f ] m a x = 75 KHz. The con-tours are plotted for peak factors c = \/20.and c = yiO". 64 5.19 PM- isopreference contours and contours of constant channel capacity for the peak frequency deviation Af m a x = 15 KHz. The contours are plotted for peak factors c= \/20 and c = JlO 65 5 . 2 0 Curves of maximum attainable scale value vs a v a i l -able channel capacity for DPCM, PCM, AM, DSB-SC, SSB-SC and PM. The parameter k represents a mea-sure of coding eff i c i e n c y 68 th A. 1 .1 An N order l i n e a r predictor 71 A.1.2 Optimum predictor coefficients cx^  -. The subscript i r e f e r s to 1, 2, or 3 intervals of time delay and j refers to. the order of the predictor 74 LIST OF TABLES Page 5.1 Comparison of Maximum Scale Values Attainable Using Discrete and Continuous Values for the Number of Bit s of Quantization L 56 5.2 Maximum Scale Values for the Fixed B i t Rates Obtained from Figures 5.16(a) and 5.16(b) 59 5-3 Mean Square Bandwidth of Speech 63 A . l Values of rg = e a ^ / e o 2 Corresponding to'Points of Maximum Discrepancy Between on and i t s Approx-imation a± (Bandwidth W>1.5 KHz) 73 A.2.1 Results of DPCM P i l o t Rating Tests 75 A. 2.2 DPCM Reference Point Rating Tests 76 A.2. 3 AM P i l o t Rating Tests 77 A. 2.4 AM Reference Point Rating Tests 77 ACKNOWLEDGEMENT Grateful acknowledgement i s given to the Defense Research Board of Canada who supported the research i n t h i s thesis under Grant DRB-66-2826, and to the National Research Council for a bursary i n 1966-67 and a studentship i n 1967-68. I am most grateful to my supervisor, Dr. R. W-. Donaldson, for his constant guidance and reassurance i n the execution of t h i s project. I wish to thank Dr. E. V. Bohn for reading the manuscript and for his valuable suggestions. I am especially thankful to Mr. Don Chan for his many helpful suggestions and for the many in f o r mative discussions which we had. I wish to .express my appreciation to Dr. M. Kharadly and Mr. R. Olsen for the -use of t h e i r anechoic chamber. Also, I wish t o thank Dr. D. Greenwood of the Psychology Department of U.B.C. for the use of his noise generator and wave analyzer. I am g r a t e f u l to the graduate students and staff members of the E l e c t r i c a l Engineering Department of U.B.C. who participated i n the l i s t e n i n g t e s t s . I also wish to thank Mr. M. Koombes for his assistance i n conducting some of the tests. I wish to thank my wife for her encouragement and for typin the o r i g i n a l draft, Miss A. Hopkins for typing the manuscript, and Messrs. J. Cavers, G. Toussaint, and N. Dykema for proofreading the f i n a l copy. 1 1. INTRODUCTION 1.1 Communications Systems A communication system may be considered to be composed of the f i v e parts shown i n Fig. 1.1. Message Signal Received_ signal Reconstructed message Inform -ation /. Trans- /. Channel /. Receiver Source mitter Fig. 1.1 A general communication system The information source produces the message to be communicated. The transmitter operates on the message to prepare i t for transmission over the channel. The channel distorts the signal p r i o r to i t s reaching the input of the receiver. The receiver reconstructs the message which i s then presented to the f i n a l receptor. The best performance measure of such a communication system i s how s a t i s f a c -tory the receptor considers the reconstructed message to be given that he ( i t ) knows exactly the o r i g i n a l message. The operation of the transmitter may be further subdivided into three basic operations: source encoding, channel encoding and modulation. In "the case of amplitude and angle modulation systems, the source and channel encoder combination consists of a l i n e a r f i l t e r . The modulators, i n these cases, vary the amplitude or the angle of a c a r r i e r according to the var i a t i o n of the message amplitude. In a d i g i t a l communication system, the pur-pose of the source encoder i s , i d e a l l y , to encode the message into a sequence of equi-probable, independent, discrete symbols. The channel encoder then 2 adds, i n a way that i s optimum for the par t i c u l a r channel and modu-l a t i o n system used, enough redundancy to keep the probability of a transmission error below some specified l e v e l . The modulator accepts the channel encoder output and generates from i t a signal suitable for transmission over the prescribed channel. The receiver demodu-lates the received sig n a l , and reconstructs a delayed r e p l i c a of the input. 1.2 Br i e f Review of Source Encoding Techniques An id e a l source encoder removes a l l redundancy from the input sig n a l . In a p r a c t i c a l system, only part of the redundancy i s removed, since the removal of a l l redundancy i s usually imprac-t i c a l i f not impossible. A measure of source encoder ef f i c i e n c y i s the amount of redundancy removed. Much work has been done on the optimization of the source encoder for pulse cod.e modulation (PCM) systems*. Several investiga-tors have been concerned with the optimization of the quantization process alone [l-4] while others have been concerned with optimizing the combined process of quantizing, sampling, . and reconstruction 5—9 Many systems which, have been proposed and investigated use feedback around the quantizer to reduce the redundancy i n the encoder output. One such system i s the d i f f e r e n t i a l pulse code modulation (DPCM) system i n Pig. 1.2. Delta modulation (AM) results when the quantizer i n Pig. 1.2 contains two output l e v e l s . Numerous investigations of DPCM have been carried out. Van de Weg [lOJ derived the signal-to-noise r a t i o as a function of the number of b i t s of quantization and the r a t i o of the sampling f r e -quency to the bandwidth for a system having a bandlimited white noise *• A PCM system results i f the feedback f i l t e r s are removed from the source encoder and source decoder i n Fig. 1.2. 3 Source Encoder Nonuniform Quantizer Feedback Filter z 5u5 1* c c fcj 1 o o 8 <L) C c o F i g . 1.2 General d i f f e r e n t i a l pulse code modulation (DPCM) system input and a single integrator i n the feedback path. Nitadori [ U j obtained the quantizer characteristic which' minimizes the quantiza-t i o n noise for speech signals when the feedback network i s an i d e a l integrator. O'Neal [ l 2 , 1 3 ] and McDonald ["14-J derived approximate formulas for the signal-to-noise r a t i o s of DPCM systems having l i n e a r predictive feedback networks. O'Neal obtained simulation results for video input signals, while McDonald obtained results for speech input signals. Irwin and O'Neal [15] derived the optimum quantizer and predictor for a Gaussian stationary wide-sense -Markov input under the assumption that the quantization noise i s Gaussian white. Donaldson and Chan [ l 6 ] have derived an expression for the s i g n a l -to-noise r a t i o as a function of the bandwidth of the message, the sampling frequency, the quantizer c h a r a c t e r i s t i c , the l i n e a r predic-t i o n c o e f f i c i e n t s and the s t a t i s t i c s of the message and channel noise O'Neal [17] , Sharma [ l 8 ] , Hosakawa, Onaga, Katusho and Kato [ l 9 ] , and Abate [20] , have considered the effects of quantization i n AM systems A complete analysis of the mean square error i n the outputs of PCM and DPCM source encoders i s s t i l l lacking. Even i f such a complete analysis were available, the ultimate evaluation of any encoding system requires subjective measurements on real-time systems Although several investigators "[21-23] have made subjective measure-ments on video systems, very l i t t l e work has been done on the sub-jective _evaluation of DPCM speech communication systems. Recently, Donaldson and Chan [ l6] , devised a technique for evaluating as a function of an arb i t r a r y number of system parameters the subjective quality of voice communication systems, and used t h i s technique to measure, as a function of speech bandwidth W and the number of quan-t i z a t i o n b i t s L, the subjective quality of PCM and DPCM speech. The sampling rate equalled the Nyquist rate i n th i s investigation. 5 Few attempts have been made to compare different voice communication systems, either on the basis of mean square difference between the transmitted and received waveforms or on the basis of subjective q u a l i t y . Comparisons of some pa r t i c u l a r systems and channels have been carried out by G-oblick [24] who compared communi-cation systems on the basis of required channel capacity for the cases of Gaussian inputs with various spectra. He pointed out that the performance of d i g i t a l systems i s l i m i t e d both by the ef f i c i e n c y of source encoding and the degree of channel interference, whereas the performances of analog systems are r e s t r i c t e d only by the channel interference. 1.3 Scope of the Thesis The work described i n t h i s thesis was conducted i n order to enable various d i g i t a l and analog voice communication systems to be compared on the basis of subjective quality. The subjective quality of the output of the system i n F i g . 2.1 was obtained as a function of the number of b i t s of quantization L, the bandwidth W, and the r a t i o r of the sampling frequency to Nyquist sampling frequency 2\» • for one sample feedback (N = 1 i n the feedback loop). It was found that an optimum choice of r, W, and L existed for a l l b i t rates R = 2r¥L. It was also found that the optimum sampling rate was the Nyquist rate, and that the improvement afforded by increasing the sampling frequency over the Nyquist rate was more than offset by the required increase i n b i t rate. The subjective effect of using more than one sample of feedback was investigated. Noise i n the feedback loop caused by dc offset errors i n the sample and hold c i r c u i t s and noise present i n the outputs of the feedback coefficient amplifiers prevented a thor-ough investigation of two- and three- sample feedback. 6 The subjective value of AM speech vs W and r was measured. The subjective quality of AM communications was measured vs W and channel signal-to-noise r a t i o , and the maximum subjective quality obtainable for a given channel was determined. A technique was then developed for using these results to estimate the subjective quality of speech transmitted by phase modulation (PM) through a channel of given noise l e v e l and bandwidth. A comparison was made of the subjective performance capa-b i l i t i e s of PCM, DPCM, AM, DSB-AM, SSB-AM and PM on an important class of communication channels. It was found that except when large channel capacities are available, SSB-SC and DSB-SC e f f e c t i v e l y out-perform AM, PCM, and DPCM. However, when large channel capacities are available, the performance of DPCM i s s i g n i f i c a n t l y better than that of DSB-SC or SSB-SC. The results also indicate that, for high quality speech communications, DPCM requires less channel capacity than does PM. 7 2. SIGNAL-TO-NOISE RATIO IN PCM, DPCM, AM, PM AND PM COMMUNICATION SYSTEMS 2.1 Signal-to-Noise Ratio i n DPCM A p r a c t i c a l DPCM system appears i n Fig. 2.1. In the f o l -lowing analysis, the d i g i t a l channel noise i s assumed to be n e g l i -g i b l e * . The sampler i s represented as a product modulator i n which the input i s multiplied by an i n f i n i t e sequence of pulses of width A and unit amplitude. The encoder transmits message s(t) = p(t) •• (e(t) + q(t)) = p(t) • ( X ] L + q) M S - h) (2.1) where the symbol * denotes convolution. The decoder receives s(t) (for n(t) = 0) y i e l d i n g an output x = r * f * g Q (2.2) where f ( t ) i s the impulse response of the system having transfer •function l / ( l - H ( f ) ) and g (t) = (2WB/f A) (sin2itWt/2itWt) i s the im-O S pulse response of the receiver lowpass f i l t e r . Combining equations (2.1) and (2.2) yields x = |p • [ ( x 1 + q)*(5" - h ) ] j * f * g Q Since p • (x *(5 - h)) * f * g - = x,/A for AB = 1 and f.>2W, £ = x±/A + [p • (q*(S- h))] * f * g Q . (2.3) The mean square error i n the output i s therefore * Although the removal of redundancy i n the transmitted b i t stream makes the received message more susceptible to channel noise, i n a properly designed system, channel errors can be made a r b i t r a r i l y small [25,26] . Encoder Channel IT Ideal Low-pass Filler Bandwidth =W Impulse Response Nonuniform Quantizer No.ofBils=L No. of Level= zL Synchronized Linear Predictor Impulse Response i'i rs Transfer Function H(f)-I«,e t-i -3a Sampling Freguency-fs Sampling Pulse Width-A r Bit Rate R-ftL J Decoder Linear Predictor Impulse Response hlD-icr-ttU) Ideal Low-pass Filter Bandwidth-W Impulse Response *>" <u I znwt i J 2.1 A p r a c t i c a l DPCM system. = (x - x-j/A) 2 + (x - x ^ A ) 2 - 2 ( £ - X l / A ) ( x - x±/A) (2.4) The l a s t term i n (2.4) equals zero and. (x - x x / A ) 2 = 2 / X(f)df 'W The power density spectrum of q*(£- h) equals Q(f) |l - H(f)j 2 and the spectrum of p'(q*(5- h) equals / , p, Q(f-kf ) 1 - H(f-kf ) s 1 ' k k=-oo s' Since the transfer function of the decoder equals B/(f A ( l - H(f))) s for -W<f<W, and since H(f-kf o) = H(f) for a l l k, by assuming impulse k' si 's' sampling (|p,/f = l ) for a l l k, (2.4) becomes e 2 = 2 / X(f)df + B 2 / Q(f-kf )df ( 2 . 5 ) In Figure 2.1 q = T(e)-e = T [ X i * ( 5 - h)-q*h] - [ x 1 * ( S - h)-q*h] (2.6) I f q (t) i s a solution to (2.6) for a given x-^(t) and i f t h i s x-^(t) i s replaced by Kx-^(t) with the quantizer c h a r a c t e r i s t i c being scaled such that q = KT(e/K), then the new value of q(t) which s a t i s f i e s (2.6) i s Kq ( t ) . Since q(t) i s therefore proportional to x-^(t) and since e(t) = x^#(5- h)-q*h i s proportional to x-^(t) , q(t) i s pro-portional to e(t) and therefore Q(f) i s proportional to e for a l l f Thus, Q(f-kf g)df = B 2 f Q e 2 (2.7) 2 where n^ i s the t o t a l noise power i n the received signal due to quan t i z a t i o n , fq i s a constant of proportionality which depends on W, f , function T and on the second order amplitude probability density of e ( t ) . From F i gure 2.1 for a = -1 e 2 = (x 1*(S- h) - q*h) 2 = [-1 - g V l ( t - i / f s } + g a i g ( t - l / f 8 ) ] - 2 [ g ° l < l ( t - !/*„)][ x L - g c c i X l ( t - i/f s)] N N N S Z «i«i R x ( ( i - j ) / f s ) + S 2 " i ^ R ( ( i - 3 ) / f s ) i = 0 j=l i=o j=i 1 J x i q S ' (2.8) where R (T) and R (T) are the autocorrelation functions of x n ( t ) and q(t) respectively and R (T) i s the cross-correlation of x n ( t ) x i q i and q ( t ) . Let 0 (T) = R (T)/x 2 , 0 (T) = R ( T ) / x 2 0 x (T) = x-| x-^  J- Q q -L Xn q R v n(T)/x 2 and X * ( f ) = X ( f ) / x 2 . Therefore, equation ( 2 . 4 ) becomes, W^ 2 / X*(f)df + f J X * ( f ) d f 'W > >~ a.a.0 ( ( i - j ) / f N N J L J L 1=1 j=l 1 = 0 J ( 2 . 9 ) When L ^ 3 , q 2 « e 2 and 10q (T)| and | 0 X q C D are much smaller than j 0x_| (T) j for most V . Under this constraint, i f fg i s 1 p p not strongly dependent on the o^'s, then e /x i s minimized with respect to the oc^ 's by choosing them to be a solution of the follow-ing set of l i n e a r equations [ 2 9 ] . 11 N = Z aiW{l-i)/iB) ( 2 - 1 0 ) This choice of the a.'s results i n 1 -^r- = 2 / x*(f)df + f Q ( / x * ( f ) d f ) ( i - a i ^ x ( l } ) ( 2 - l l } x 2 Jw J-W i = l 1 s When the input to the quantizer i s a speech waveform, the quantizer i s usually constrained to be logarithmic. When u, the logarithmic quantizer parameter, i s large compared to the ratio.of the peak to root-mean-square value of the input, the d i s t o r t i o n i s largel y independent of the input signal s t a t i s t i c s [4] . Under th i s constraint f Q ^  ^  [log(l+|_i)] 2 4 ~ L for L > 3 and f g = 2W . Therefore 'equation (2 . 11 ) becomes ~i- = 2 Ax*(f)df + (l/3)[log(l+n)]2 f X * ( f ( d f ( l + f ] a i 0 x i ( V f s ) ) 4 - L ( 2 . 1 2 ) When the optimum L £ 3 , the assumptions |0 (T) « 0 (T) ' x-j^ q X T and 0 (T) « 0 (T) x l 1 no longer apply with the result that evaluation 2 of e becomes d i f f i c u l t . 2 . 2 The Effect of Sampling at Higher than the Nyquist Rate Sampling at frequencies greater than the Nyquist rate has three effects: A l i a s i n g errors and i d l e channel noise [*14] caused by non-ideal lowpass f i l t e r s are reduced; an improved prediction of the sampled input r e s u l t s ; and the amount of quantizer noise l y i n g i n the passband of the receiver lowpass f i l t e r i s reduced. By res-t r i c t i n g the minimum sampling frequency to be 2 . 2 times the 3 db cutoff frequency of the input lowpass f i l t e r , the effects of a l i a s i n g 12 errors and i d l e channel noise are largely eliminated. To see that an increase i n sampling frequency increases the p r e d i c t a b i l i t y of the sampled input, consider the normalized autocorrelation function of speech i n Figure 4.2. It i s seen that an increase i n sampling frequency results i n an increase i n correlation between the input and i t s delayed r e p l i c a provided f >, IKHz, which i s v i r t u a l l y always the case. In Appendix I i t i s shown that such an increase i n correlation results i n an improved prediction of the input signal. This correspondingly means a reduction i n mean square input to the quantizer which, by equation (2.7), indicates a reduction i n received quantization noise. Fig. 2.2 (a) Spect rum of quantization noise, (b) Quantizing noise a l i a s i n g due to sampling. Co) Output quantization noise. Note that increasing f decreases the contributions due to a l i a s i n g . s In order to i l l u s t r a t e the t h i r d effect consider equation (2.7) reproduced here i n part for convenience. 13 n 1 C O Q(f - kf )df (2.13) Since the bandwidth of the quantization noise exceeds the signal bandwidth [28,29], an increase i n f results i n a reduction i n the t o t a l quantization noise d i s t o r t i o n i n the system output.(see F i g -ure 2.2). Note that i f f = 2W, equation (2.13) becomes n B 2 / Q(f)df = q 2B 2 2.3 Signal-to-Noise Ratio in AM Communication The essential features of a double-sideband suppressed c a r r i e r amplitude modulation system (DSB-SC) appear i n Figure 2.3(a). The lowpass f i l t e r H(f) i s assumed to be ide a l with char a c t e r i s t i c as i l l u s t r a t e d i n Figure 2.3(b). The modulating frequency f 1 = U)Q/2x i s re s t r i c t e d to being greater than 2W. The channel noise n (t) i s w assumed to be additive white Gaussian with power density spectrum S (f) = N /2 n. - O O wcos U.i Lowpass Filter x,(t) t w <f < ^ n w c t ) 4 -Lowpass F i l t e r w \ -w ( b ; w X<0 Fig. 2.3 (a) A double sideband suppressed-carrier amplitude modulation system, (b) Ideal lowpass f i l t e r charac-t e r i s t i c (c) Assumed power spectrum of the baseband input signal. Let X ( f ) , the power spectrum of the baseband input signal x ( t ) , be as shown i n Figure 2.3(c). The mean square error i n the output i s ? = (x(t) - 2 ( t ) ) 2 = (x - x 1 ) 2 + n 2 - 2(x - x 1 ) n . (2.14) The l a s t term i n (2.14) i s zero. Also A C X 3 (x - x-,) 2 = 2 / X(f)df . (2.15) The power spectrum of 2coscoQt • n (t) i s the convolution of S (f) w with two impulses of magnitude l/2 placed at ~fQ, and i s equal to S ( f ) . Therefore, the second term on the right side of (2.14) nw becomes N N" W n 2 ( t ) = ^ / ^ df = (2.16) A , u -W Combining (2.14), (2.15) and (2.16) yields WN ^ 2 ( t ) = 2 / X(f)df + -f- ' (2.17) -V A . Since the transmitter signal power i s P s = x 2 = / X t ( f ) d f = A 2 / X(f)df the inverse signal-to-noise r a t i o for AM communications becomes ( | ) A M = -ZT- = 2/ X * ( f ) d f + f ^ /X*(f)df (2.18) x 2 ^ W s J-W 15 O O where / X*(f)df = 1. 2.4 Signal-to-Noise Ratio i n Angle Modulation Systems*. Angle modulation systems are divided b a s i c a l l y into two categories; phase modulation (PM) and frequency modulation (FM). In the following analysis, phase modulation i s presented as a special case of frequency modulation. The difference between the two i s i l l u s t r a t e d i n Figure 2.4. \njt) x(t) H/f) */1) FM_ FM Transmitter - J I T 1 ^ H/f) ,«W. L imiter -Discriminator HIF(f) HRF(f) r(t) PM kH< (f) (a) - 1 V. w f IF -Wc (b) Fig. 2.4 (a) Angle modulation systems, (b) Characteristics of the ideal RF (H R p) , IF (H-^ -p) and lowpass (H^) f i l t e r s . The frequency characteristics of the lowpass f i l t e r H^(f), the radio frequency (RF) bandpass f i l t e r H R F ( f ) and the intermediate frequency (IF) f i l t e r H-j--p(f) are also shown i n Figure 2.5. Again, * The following analysis i s necessarily very s i m p l i f i e d . For a more complete analysis of angle-modulation systems the reader i s referred to Sakrison [3l] • 16 the f i l t e r s are assumed i d e a l , and the channel noise i s assumed to be. additive with a spectrum which i s uniform over the channel band-width. The PM transmitter generates from the lowpassed input an output x t ( t ) = Al/£"cos2ir(fot + W p M ^ c 1 ( t ) d t ) where Wp^  [x-^(t)| m a x i s the peak frequency deviation. The received signal r ( t ) i s f i r s t bandpassed through H^p(f), multiplied by \/l cos2icf^t and then passed through H^p(f). In the absence of noise, the input to the limiter-discriminator i s then f x ( t ) = A cos2jtJf2t + WFM / x 1 ( t ) d t j With r^ ( t ) as i t s input, the l i m i t e r - d i s c r i m i n a t o r , a device which extracts and d i f f e r e n t i a t e s the instantaneous phase of i t s input, produces an output r 2 ( t ) = d/dt[2icW p M^c 1(t)dt] . = (2jtW p M)x 1(t) After passing through an attenuator of gain 1/2^^, the output of the demodulator for noise-free transmission i s x-^(t), the lowpassed input signal. I f now the assumption of noiseless transmission i s removed, and i f the input to the frequency modulator i s assumed constant 'for a short period of time* X l ( t ) = x Q, -\<x<\ then the input to the limiter-discriminator becomes r-^t) = a(t)cos(2:t(f 2 + ^ m ^ Q ) t + 9(t)) * This amounts to approximating the- message by a s-eries of rectangular pulses of width A. As A becomes small compared to l/2W the approx-imation becomes more exact. 17 where a(t) = 1/(A + n ( t ) ) 2 + n 2 ( t ) ' c s and 9(t) = t a n - 1 ( - n (t)/(A + n (t))) . s c In these equations n (t) represents that component of the noise i n phase with cos ( 2 i t ( f 2 + Wpjypc )t) a n& n s ^ ^ that i n phase with sin ( 2 r c ( f 2 + W-p^x^t). The power density spectra of n c ( t ) and n (t) are equal to the even part of S (f - - Wj>]y[x0) [25] . If one 2 assumes that 2N W « A , then the approximation 0(t) = -n ( t ) / A i s o s v a l i d except for certain improbable and hence infrequent instances of time. Recalling the effect of the limi t e r - d i s c r i m i n a t o r , i t may now be seen that the output of the system after attenuation and low-pass f i l t e r i n g i s A . x(t) = X l ( t ) + n Q ( t ) The power density spectrum of n (t) i s given by S n (f) = ( l / 2 r t A W p M ) 2 S n ( f ) | H 1 ( f ) | 2 | j 2 3 r f | 2 . ( 2 . 1 9 ) It follows that the noise power i s concentrated i n the higher f r e -quencies. Consider now the power spectrum of the noise output of a phase modulation system; (f) =Cl/atAW ) 2S r i (f)|H, (f) 2 I J27tf 2 l / j 2 ^ f | 2 ( 2 . 2 0 ) noPM s Note that t h i s power spectrum i s uniform across the message bandwidth, From ( 2 . 1 9 ) and ( 2 . 2 0 ) , the output noise powers of FM and PM are %2 = (l/W F M) 2(N oW/A 2)(W 2/ 5: and n Q 2 M = aAtW p M) 2(N QW/A 2) . The transmitter power i s given by 18 P = x t 2 ( t ) = A 2 Combining the above equations y i e l d s the inverse s i g n a l - t o - n o i s e r a t i o s f o r PM and PM: ( | ) F M = 2/ X*(f)df + (-r=r)^)(^-) (-f-)/ X*(f)df (2.21) 2 N ¥. r W (|)pM = 2 X*(f)df + ( ^ ( ^ " V ( ^ ) / X * ( f ) d f (2.22) X * ( f ) d f = 1. O O The channel bandwidth Wc r e q u i r e d f o r angle modulation com-munication may be w r i t t e n approximately as [30J Wo = M m a x + 2 W < 2 - 2 3> where l^f | x 1 S a measure of the maximum instantaneous frequency d e v i a t i o n . The instantaneous frequency d e v i a t i o n f o r PM i s ( A f ) F M = W F M x x ( t ) and f o r PM i s ( A f ) p M = W ^ x ^ t ) . . . [==* Since the p r o b a b i l i t y that |x-^(t)| exceeds cvx^ (t) may be made small by choosing the peak f a c t o r c l a r g e , an approximate expression f o r WcFM 1 S ' T.T _„ 2"' WcPM = C W P M ^ x 1 + 2 W c r i ' i rm A l s o , and f o r PM W c p M = c W ^ y / x ^ + 2W. 1^. = (4x2J f 2 X 1 ( f ) d f ) 2 = 2jtv/xn d V f ^ 1 m 19 where 2 V A f r=f I j L ^ f x 1 ( f ) d f \ * A V f = - rms bandwidth of the m \ ^oo ) X ^ ( f ) d f message Therefore, (2.21) and (2.22) may be r e w r i t t e n w • r°° 2 W2 • /N w r W (|)PM = 2 / X * ( f ) d f + S_W (_2_) / X * ( f ) d f (2.24) 3(W c F M-2W) 2 J _ w •N o2 f 2(W) NW r W (|) p M = 2 / X * ( f ) d f + ^ ( _ o _ y i x » ( f ) d f ( 2 < 2 5 ) 20 3. REAL TIME DPCM AND AM SYSTEMS 3.1 A Real Time DPCM System I f i t i s assumed that the channel noise i n F i g . 2.1 i s n e g l i g i b l e , then the output x ( t ) of the system shown i n F i g . 3«1 i s equivalent to the output x ( t ) of the system i n F i g . 2.1. A p r a c t i c a l r e a l i z a t i o n of the system i n F i g . 3.1 A system equivalent to F i g . 2.1 when channel noise i s neglected. F i g . 3-1 f o r N = 3 i s shown i n F i g . 3-2. Only the general opera-t i o n of t h i s system w i l l be described here. For d e t a i l s of the c i r -c u i t s used, the reader i s r e f e r r e d to Chan [32]. Assume the system i s i n i t i a l l y i n i t s quiescent s t a t e . The a r r i v a l of a clock pulse i n i t i a t e s the tim i n g sequence; r e s e t , pulse 1, pulse 2, .... pulse 8 (only to pulse 3 i f f s £ 2 1 . 5 KHz ) . The reset pulse actuates the input sample and hold (S & H) and the output feedback S & H's. The input S & H samples the low-pass f i l t e r e d speech and stores the current value. At the same •Nonuniform Quantizer L r 1 1 i Com-pres-sor Uniform Quantizer L Bits Ex-pand-or 1 1 Output Feed-back S&H2\ 7? Output Feed-back S&H3 •-4—-8> Input Feed-back S3Hf Samp-ler Low-pass Filter W -Linear Predictor Master Clock R R P> P? 1 ft f M facet '• '• PUIMZ Timing. Pulse Generator M=3 or 8 F i g . 3.2 An implementation of F i g . 3.1 f o r N = 3. 22 time, the values c u r r e n t l y being held by the input feedback S & H's are m u l t i p l i e d by the p r e d i c t i o n c o e f f i c i e n t s , a^, and ct^ (see Appendix I ) , sampled and stored i n the corresponding output feedback S & H's. The sum of the outputs of the three output feed-back S & H's i s now an estimate of the current input sample. The a c t u a l and predicted values are now subtracted and t h e i r d i f f e r e n c e nonuniformly quantized. The values c u r r e n t l y being held i n the f i r s t and second of the s t r i n g of output feedback S & H's are now s h i f t e d to the second and t h i r d feedback S_& H's respec-t i v e l y . The quantized d i f f e r e n c e s i g n a l i s added to the predicted value and the sum i s stored i n the f i r s t of the s t r i n g of input feedback S & H's. The sum i s a l s o sampled and lowpass f i l t e r e d . The r e s u l t a n t lowpass f i l t e r output x ( t ) i s then a r e p l i c a of the o r i g i n a l speech s i g n a l x ( t ) . The system parameters W, f s , L and a ^ ( i = 1,2,3) are v a r i a b l e , as are the compressor and expandor c h a r a c t e r i s t i c s . 3.2 Disadvantages of the System Used Consider the i n t e g r a t o r network i n F i g . 3*3 where n-^(t) i s a noise input which may be considered to represent noise caused by the d e l a y i n g and a t t e n u a t i n g c i r c u i t r y . For y ( t ) = 0 , the power spectrum of the output i s given by N n ( f ) 1 - a where N, (f) i s the power spectrum of n-,(t). I t f o l l o w s that 23 F i g . 3 . 3 An i n t e g r a t o r network. f o r a a p p r o a c h i n g u n i t y , any s m a l l amount of n o i s e g e n e r a t e d w i t h i n the p r e d i c t o r w i l l be a m p l i f i e d g r e a t l y . C o n s i d e r now the complete system of F i g . 3 - 2 . As shown . i n Appendix I , the sum of oc^, , and oc^ approaches u n i t y . Except .for the f a c t t h a t the n o i s e i s now b e i n g g e n e rated by t h r e e a t t e n u -a t i o n and d e l a y networks, the s i t u a t i o n i s v e r y s i m i l a r t o t h a t d i s c u s s e d above when N = 1 , except t h a t the p r e d i c t o r n o i s e , a f t e r b e i n g q u a n t i z e d , s h o u l d be s u b t r a c t e d from the output of the output summing a m p l i f i e r . I f the q u a n t i z e r has v e r y few b i t s , the q u a n t i -z a t i o n n o i s e may be v e r y l a r g e , and v i r t u a l l y u n c o r r e l a t e d w i t h the p r e d i c t o r n o i s e . As a r e s u l t , the feedback n o i s e w i l l s t i l l be heard at the o u t p u t , a l o n g w i t h l a r g e amounts of q u a n t i z e r and i d l e c hannel n o i s e [ l 4 J . N o r m a l l y , a s m a l l DC b i a s i s added t o the i n p u t s i g -n a l w i t h the r e s u l t a n t i d l e c h a n n e l dominant mode o s c i l l a t i o n b e i n g removed by the output lowpass f i l t e r . However, i f the q u a n t i z a t i o n i s f i n e , the s m a l l DC b i a s i s overcome by p r e d i c t o r n o i s e , w i t h the r e s u l t t h a t the i d l e c h a n n e l n o i s e may not be e l i m i n a t e d by the o u t -put lowpass f i l t e r . As a consequence of t h i s n o i s e b u i l d u p , i t was e x t r e m e l y d i f f i c u l t t o o b t a i n s u f f i c i e n t l y r e l i a b l e r e s u l t s - w h e n two and t h r e e 24 samples of feedback were used. Therefore, the experiments des-cribed l a t e r were conducted f o r only the previous sample feedback case. 3.3 Measurement of AM Signal-to-Noise Ratio The system shown i n F i g . 3.4 was used to simulate an Am communications system. For n (t) white Gaussian noise, the output x(t). F i g . 3-4 A system whose output i s equivalent to the DSB-SC system i n F i g . 2 .3(a) f o r A = 1 . of t h i s system i s i d e n t i c a l to the output of the DSB-SC system shown i n F i g . 2.3 w i t h , -of course, an appropriate s c a l e f a c t o r to account f o r the gain A i n F i g . 2.3» The s i g n a l - t o - n o i s e r a t i o at the output of t h i s system may be w r i t t e n S N where denotes a time average over a l l time. The speech sample used f o r the t e s t s described i n Chapter IV may be w r i t t e n x (t) = m (t) 0 0 < t ^  T elsewhere Therefore, the time average power of the received message i s approx-imated as f o l l o w s : 25 x 2 0(t) rn (t) dt, A s i m i l a r equation may be used to estimate the received noise power. Although the d e f i n i t i o n of the mean s p e c i f i e s an i n t e g r a l over a l l time, r e s t r i c t i n g the i n t e g r a l to a f i n i t e i n t e r v a l of time does not introduce a la r g e e r r o r i f the i n t e r v a l i s large•compared to the durat i o n of the a u t o c o r r e l a t i o n f u n c t i o n of the input [ 3 3 ] . The c a l c u l a t i o n of the time average power was performed on an EAI PACE 231R Analogue Computer using the c i r c u i t shown-in P i g . 3»5. The output of t h i s system i s v (t) = 10,000a 2 / v2(\)&% 0 J0 1 The mean square value of the input i s then given by V q ( T ) v 10,000a T variable potentiometer-Ckvarter-s^ care Integrator ) Multiplier X l//oo F i g . 3-5 C i r c u i t f o r measurement of mean square power. Since the speed of tape on which the sentence was recorded was 7T inches per second, the duration of the speech sample T could be c a l -culated by measuring the length of the tape on which the sample was recorded. This length was found to be 15^ .5 inches resulting in T =2^.06 seconds. The measurements i n a l l cases were averaged over f i v e r e p e t i t i o n s to minimize the e f f e c t of any random disturbances or ti m i n g inaccuracies. The r e s u l t a n t s i g n a l - t o - n o i s e r a t i o was c a l c u l a t e d as fol l o w s o v (T ) 10,000a2T S _ os s '_ n n N ~ , n n n A 2™ * v (T ) 10,000a T on n ' ' s s 2 a v 7.5 ±6$ n - 5 S (2) 2 v^  (15) a s on where the s u b s c r i p t s s and n r e f e r to the speech and noise r e s p e c t i v e l y . 27 4. SUBJECTIVE TEST PROCEDURE 4.1 Introduction Many methods have been developed to quantitatively scale perceptual s t i m u l i [34] • The results presented i n Chapter 5 are based on a modification of the paired comparison method [35] • This method was used to obtain equal preference (isopreference) contours, and these contours were then scaled using a version of the subjec-tive-estimate method. Although either method could have been used to both deter-mine and to rate the isopreference contours, more r e l i a b l e results are obtained by using a composite of the two. A rating scale derived by use of the paired comparison method i s unreliable whenever the v a r i a b i l i t y of the l i s t e n e r s ' judgements i s not substantial. The subjective-estimate method requires l i s t e n e r s to judge how much better one stimulus i s than another. This method also requires the experimenter to extrapolate between the scale values of the test •points, since the rated points may not necessarily l i e on any par-t i c u l a r isopreference contour. For these two reasons, the subjec-tive-estimate method does not y i e l d r e l i a b l e isopreference contours. The master sentence used throughout the tests was recorded i n an anechoic chamber using a General Radio Type 1560-P3 PZT micro-phone and a Tandberg 64X tape recorder. The sentence "Joe took father's shoe bench out" was chosen as the master sentence since i t contains most of the phonemes and has a frequency spectrum which i s representative of conversational speech [36] . The sentence was spoken by a 28 year old male with a Western Canadian accent. An estimate of the speaker's spectrum obtained using the method des-cribed i n Section 3-3 appears i n Figure 4.1. 28 2.01 0 1 2 3 4 5 6 7 Frequency (KHz) F i g . 4.1 Power den s i t y spectra of speech. 29 4 . 2 Preparation of Speech Samples The speech samples were obtained by playing back the master sentence through the appropriate system (either DPCM or AM) and re-recording on a second Tandberg 64X tape recorder. The samples were then spliced together along with appropriate lengths of non-magnetic tape. In order to eliminate hum present at the tape re-corders' outputs, a l l tape playbacks were high-pass f i l t e r e d to approximately 200 Hz. 4 . 2 . 1 DPCM Samples In the preparation of the DPCM samples, the following assumptions and r e s t r i c t i o n s were imposed: (1) The d i g i t a l channel noise shown i n Figure 2 . 1 equalled zero. (2) The nonuniform quantizer was constrained to be logarithmic with LI = 1 0 0 . Panter and Dite [ 4 ] have shown that.with logar-ithmic compression, the resultant d i s t o r t i o n i s r e l a t i v e l y independent of the input s t a t i s t i c s assuming the peak value of the input does not exceed the maximum quantizer input. (3) The amplitude of the input signal was always adjusted u n t i l the quantizer input occupied the f u l l available range of the quan-t i z e r . (4) For minimum mean square error, the prediction c o e f f i c i e n t was determined from equations ( 2 . 1 0 ) to be equal to the normal-ized autocorrelation of the speech signal evaluated at the samp-l i n g period. However, equations ( 2 . 1 0 ) presuppose r e l a t i v e l y fine quantization as well as an exact knowledge of the autocor-r e l a t i o n function of the speech sample being processed. As a res u l t , the approximate relationship for oc^  shown i n Fig. 4 . 2 was used. Also shown i n this figure are autocorrelation func-.o o o o <v .N 04 02-0 -02-Autocorrelation Function from McDonald [14] Autocorrelation Function obtained by taking the Fourier Transform of the Speech Spectrum from French & Steinberg [35] Autocorrelation Function obtained by taking the Fourier Transform of the Speech Spectrum from French & Steinberg Lowpassed at 1 KHz Autocorrelation Function Approximation for all Speech Samples in the Listening Tests -a 4? 07 0.2 0.3 0.4 0.5 0.6 0.7 Sampling Period 1/£ (ms) 0.8 Fig. 4.2 Autocorrelation functions of lowpass f i l t e r e d speech versus the sampling period l / f . 31 tions of speech based on other data, as well as an estimate of the autocorrelation function of the master sentence used. An analysis of the error encountered using the approximation i n Figure 4.2 appears i n Appendix I. ' (t) In order to eliminate a l i a s i n g errors and i d l e channel•oscilla-tions' [14J , the minimum permitted sampling frequency was r e s t r i c t e d to 2.2 times the 3 db cutoff of the lowpass f i l t e r . (6) The speech bandwidth W could assume only the discrete values of 1.01, 1.21, 1.55, 2.12, 2.63, 3.17, 4.2 and 6.3 KHz. 4.2.2 AM Samples . In the preparation of the AM samples, i t was assumed that the operations of modulation and demodulation were completely noiseless and that the channel noise was f l a t . The spe.ctrum of the output of the Grason-Stadler noise generator used was measured on a wave analyzer and was found to be f l a t to within -0.4 db' over the frequency range 200 Hz <f <6.3 KHz. The magnitude of the master sentence input Was adjusted so that the resultant integrated value of the output of the system introduced i n Section 3-3 was equal to 100 -1 v o l t s . 4•3 Paired Comparison Tests for Determining Isopreference Contours 4.3-1 Paired Comparison Tests The paired comparison tests were conducted over periods spanning f i v e days for DPCM and two days for AM. Two sessions took place each day, one i n the morning and one i n the afternoon. The ten li s t e n e r s present during any given session were selected from a group of 28 graduate students. Most l i s t e n e r s sat for fewer than eight sessions. The subjects' ages ranged from 21 to 30 with a mean of approximately 25. The tests were conducted i n a quiet room 32 using binaural hearing with Pioneer model SE-1 stereo headphones. At the beginning of each session, the l i s t e n e r s were given response forms with the following set of written instructions: "In t h i s test, you w i l l hear pairs of sentences; each pair i s separated by a 5 second rest period. After l i s t e n i n g to a pair, specify which sentence you would prefer to hear. I f both sentences sound equally good, make an arbitrary choice. The f i r s t sentence of each pair i s sentence A, and the second, sentence B." Sentences A and B were separated by a one second silence. During each session the l i s t e n e r s were required to compare between seventy and eighty pairs of sentences with a two to three minute rest, per-iod a fter every twenty comparisons. The entire set of comparisons (AM or DPCM) were heard i n random order. Each comparison appeared twice, with the order of the comparison i n the second test being reversed from that i n the f i r s t . Most l i s t e n e r s were acquainted with the speaker of the sentence. 4.3.2 The method of Paired Comparisons The method of paired comparisons i s based solely on the subjects' a b i l i t y to judge which of two conditions he prefers. The method makes four basic assumptions: the sample of subjects i s chosen from a normal population; any previous paired comparison tests have negli g i b l e effect on the test i n progress; the variable para-meter i s available as an underlying continuum; and the judgements are t r a n s i t i v e . The l a t t e r property i s discussed i n Section 4-5. As an example of the use of the method of paired compar-isons to develop isopreference contours, consider the points marked A and B i n Fig. 4-3- The sample corresponding to point A i s compared to samples corresponding to the points marked b ^ ( i = 1,2,3,4), each, of which has the same abscissa value Xg. The results of the compar-isons are plotted on a psychometric curve as shown i n Fig. 4.4(a). The ordinate of th i s figure shows the percentage of judgements pre-f e r r i n g sample A to samples having a value of the X parameter equal to X-g and the values of Y indicated i n the plot. The Y ^ ( i = 1,2,3,4) are selected such that the percentage preferring A varies from 0 to. 100$. A smooth curve i s then drawn through the experimental points and the 50$ or equal preference point Y-g plotted as the ordinate of point B. Fig. 4.3 An isopreference curve. Points b . ( i = 1,—4) are compared to point A and the results of the comparisons used to determine point B. Points A and B are now assumed to be equal i n preference. Either point could therefore be used to obtain further isopreference points. However, the discrete nature of the values of parameters (W and L) used i n the l i s t e n i n g tests dictated the use of the same reference point to obtain a l l of the isopreference points on any one contour. In p l o t t i n g the psychometric curves, i t was found that a normal d i s t r i b u t i o n curve f i t t e d the data points. The proportion of l i s t e n e r s preferring the reference sentence was therefore con-verted to unit normal deviates. Since unit normal deviates corres-ponding to 0 and 100$ are i n f i n i t e , these values were changed to 34 Value of Parameter Y for the Sample being Compared to Reference Point A (a) Fig. 4 . 4 (a) A psychometric curve corresponding to the derivation of point.B i n Fig. 4 . 3 -(b) The curve of (a) with the ordinate i n unit normal deviates. a 35 0.5 and 99-5$ before being converted. Using a weighted least squares technique, a straight l i n e was f i t t e d .to the data points. The weight attached to each deviate Y^ was given by [l6J W\ = N±e X i /-2%Vi{l-V±) where i s the number of judgements on which Y^ i s based and p^ i s the proportion of judgements preferring the reference sentence. The psychometric curve of Figure 4.4(a) i s shown plotted i n Figure 4.4(b) i n unit normal deviates. The 50$ point of Figure 4.4(a) corresponds to zero unit normal deviates. The reciprocal of the slope of the l i n e i s equal to the standard deviation cr of the points f i t t e d by the l i n e . The standard deviation associated with each point obtained i s indicated by the length of the straight l i n e through the point. 4.3.3 Selection of Test Points and Derivation of Isopreference  Contours Since, i n the DPCM case, the number of available indepen-dent parameters was three, i t was necessary to obtain isopreference surfaces. The obvious approach was to select a series of planes perpendicular to one of the axes, and to obtain isopreference con-tours within these planes. These curves could then be extrapolated from plane to plane to obtain isopreference surfaces. However, this procedure has the disadvantage that, for each isopreference surface, only one contour passes through the reference point. Since re f e r -ence points are the most r e l i a b l e points available on any contour, i t i s also desirable that the reference point be situated towards the midpoint of each contour to eliminate the effect of "pivoting" a contour about one of i t s end points. By deriving contours i n the f i v e planes indicated i n Figure 4.5, the above disadvantages were largely eliminated. The f i v e planes are defined by the following equations: plane A plane B plane C plane D plane E Fig. 4.5 Five planes passing through a reference point (P) . The abscissas i n planes D and E are indicated i n the figures with d = W l/l + k 2 and x = W l/l + m2'. Once the reference points were-selected, the planes could then be defined and the required compar isons determined. r = const = r 0 - W ~ const' = ¥ 0 - L = const = • L 0 r = kW k = r /¥ o' 0 r = mW + b b = r o o In order to obtain an estimate of the shape of the i s o -pref erence surfaces, some p i l o t tests were conducted using the subjective-estimate method to be described i n Section 4.5.-- These results were then used as guidelines i n deciding which parameter should be the variable i n the paired comparison tests. If the p i l o t curves indicated that by varying parameter A the number of l i s t e n e r s preferring the reference point would vary more rapidly than by varying any other parameter, the parameter A was varied. 4.4 Scaling of Isopreference Contours A test based on the subjective estimate method was used to assign a meaningful value to each of the derived isopreference contours. The method permits the derivation of a scale based d i r -ectly on the l i s t e n e r s ' own quantitative estimates of the quality of a sentence. The tests were conducted i n two parts. At the beginning of the f i r s t part, the l i s t e n e r s received the following written instructions: "In t h i s test you w i l l hear pairs of sentences; each pair i s separated by a 5 second rest period. I f zero denotes a sentence which i s just u n i n t e l l i g i b l e , and 10 denotes the f i r s t sentence (sentence A), rate the second sentence (sentence B) on an equal i n t e r v a l (0 to 10) scale on the basis of overall quality." A one second silence occurred between sentences within a pair. Sentence A was chosen to be the master sentence bandlimited to 6.3 KHz and re-recorded. In the second part of the tests, the order of presen-tation of the sentences within each pair was reversed i n order to. eliminate l i s t e n e r bias. In the second part, the l i s t e n e r s received instructions s i m i l a r to those i n the f i r s t part. 38 The r a t i n g tests were conducted i n groups of 30 to 40 samples with two to three minute rest intervals at the end of each ten samples. Prior to each session, the li s t e n e r s were asked to rate a series of fi v e sentences spanning approximately the f u l l range of scale values. This served to f a m i l i a r i z e the l i s t e n e r s with the range of quality 'to be expected. The tests were conducted i n a quiet room using binaural l i s t e n i n g with stereo headphones. The l i s t e n e r s were selected from the same 28 graduate students used i n the paired comparison tests. The number of subjects used varied from 10 to 15 with 5 subjects l i s t e n i n g at one time. Rating tests were performed i n four groups. The f i r s t group consisted of 116 samples used to obtain p i l o t curves for the ensuing DPCM isopreference tests. These were followed by the rati n g of 23 DPCM samples some of which were l a t e r used as reference points. These tests also included the rating of some two and three sample feedback DPCM sentences. The t h i r d group, an AM p i l o t run, consisted of 32 ratings. On the basis of these, 40 more AM samples were rated i n order to obtain reference points for the AM isopreference contours. Some DPCM points were also rated i n th i s l a s t group for purposes of comparison.. The results of a l l rati n g tests are tabulated i n Appen-dix I I . The scale value assigned to each rated sample was taken as the mean of the l i s t e n e r s ' ratings. The sample standard deviation was used as a measure of the v a r i a b i l i t y of the obtained scale value. 4.5 T r a n s i t i v i t y Checks If a point A i s judged to be equal i n preference to a point B and to a point C, then the method of isopreference testing presup-poses that i f B i s compared d i r e c t l y to C, i t w i l l be found equal i n preference to point C. Although extensive tests were not con-ducted to check t h i s assumption, an indication of th i s property of t r a n s i t i v i t y was obtained i n the following way. Some samples corresponding to AM reference points were used to obtain equal preference DPCM points. The scale values of the AM reference points used were then compared to the scale values of the DPCM reference points associated with the isopreference con-tours closest to the derived. DPCM point. The s i m i l a r i t y of these AM and DPCM scale values indicates the t r a n s i t i v i t y of the res u l t s . In a s i m i l a r way, some samples corresponding to DPCM reference points were used to obtain equal preference AM points and the corresponding scale values were then compared. 40 5. RESULTS, EVALUATION AND CONCLUSIONS 5.1 Results of the DPCM Subjective Tests 5.1.1 Determination of the DPCM Isopreference Surfaces The data obtained from the DPCM subjective tests are shown in Figures 5.1 to 5.5. The standard deviation associated with each data point equals the length of the l i n e drawn through the point p a r a l l e l to the axis along which i t i s measured.' The scale values of the reference points (indicated by s o l i d markers) are shown. Also shown are the standard deviations associated with each of the scale values. Each contour i s assigned the scale value of the r e f -erence point through which i t passes. Figures 5.1 to 5-5 correspond to the sets of planes men-tioned i n Section 4.3.2. The' f i v e contours appearing i n each figure do not a l l l i e on a constant-parameter plane and therefore w i l l not necessarily have the same general shape. This i s i l l u s t r a t e d i n Figure. 5.5 i n which the wide range of shapes i s due to a large var-i a t i o n i n the orientation of each of the planes with respect to the r and W axes. • The curves drawn i n these figures should be considered as f i r s t i t e r a t i o n s to the contours obtained by the intersection of the isopreference surfaces with the above mentioned planes, since each of the sets of curves, as well as being self-consistent, must also be con-sistent with the other four sets of curves. To develop t h i s consis-tency, Figures 5.1 to 5.5 were used to derive isopreference contours i n planes of constant W, L and r. The p r i n c i p l e advantage of choosing planes for which one parameter i s held constant i s that the shape of any one contour supplies an estimate of the general shape of the ad-jacent contours within that plane. Also, at least one of the con-tours appearing i n Figures 5.1 to 5-3 appears i n each of the 41 Bandwidth W (KHz) • F i g . 5 - 1 Isopreference contours i n L = constant planes ( L i s the number of b i t s of q u a n t i z a t i o n ) . The sc a l e value s and standard d e v i a t i o n c associated with each contour i s shown next to the reference point through which that contour passes. 42 Ratio of Sampling Frequency to Nyquist Rate r = fsj2W Fig. 5.2 Isopreference contours i n W = constant planes (W i s the bandwidth). The scale value s and standard deviation o~ associated with each contour i s shown next to the refer-ence point (drawn solid) through which that contour passes. 43 c .5 to I C3 Q 42 o OJ I Bandwidth W (KHz) F i g . 5.3 Isopreference contours i n r = constant planes (r i s the r a t i o of the sampling frequency f s to the Nyquist ra t e 2W). The scale value s and standard d e v i a t i o n & associated with each contour i s shown next to the reference point (drawn s o l i d ) through which that con-tour passes. 44 F i g . 5-4 Isopreference contours i n planes defined by equations of the form r = kW. The scale value s and standard d e v i a t i o n 6- associated with each contour i s shown next to the reference point (drawn s o l i d ) through which that contour passes. 45 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Distance along d-Axis d= W j// +mz ' F i g . 5.5 Isopreference contours i n planes defined by equations of the form r = mW + b. The scale value s and standard d e v i a t i o n associated with each contour are shown next to the reference point (drawn s o l i d ) through which that contour passes. 46 p a r t i c u l a r planes chosen. Since such contours are defined d i r e c t l y by data points, they are given the most weight i n developing the general shape of curves appearing i n that plane. The method of deriving a curve i n one plane from curves appearing i n other planes i s as follows. Assume i t i s desired to obtain a contour of scale value s =3-87 i n a plane for which the ra t i o of sampling frequency to Nyquist rate i s held constant, say r = 1.65- The method i s based on finding the intersection points of the r = 1.65 plane with the s =3.87 contours i n each of the planes of Figures 5.1, 5.2, 5.4 and 5-5. These points of intersection are indicated by the points labe l l e d A,B,C,D i n the four planes and are plotted i n Figure 5.8. Isopreference curves i n each set of planes corresponding to W, L or r should be s u f f i c i e n t to define an isopreference surface. However, although the contours within any one plane should now be consistent within that plane, they may not necessarily ,be consistent with adjacent planes, and with isopreference curves i n the other two sets of planes. This d i f f i c u l t y i s overcome by using two of the three planes to i t e r a t i v e l y update the curves i n the t h i r d plane. A f i n a l set of contours so obtained i s shown i n Figures 5.6 to 5-9. In Figures 5-10 and 5.11, the intersections of the isopref erence sur-faces with planes defined by W = 2.12 KHz and L = 4 are shown. Figure 5.12 shows an isopreference surface. 5.1.2 Discussion of the DPCM Curves and Surfaces If i n any one of Figures 5-6 to 5.9, the value of L i s increased along a l i n e of constant W, a region i s reached i n which a further increase i n L does not result i n a substantial increase i n scale value. In this region, the quality i s primarily determined by speech bandwidth. Note that for a larger value of r, this region 47 Numb&r of &i(s of Quantization L Fig. 5-6 F i n a l isopreference contours and contours of constant b i t rate i n the r = 1.1 plane. The scale value s or bi t rate R associated with each contour i s shown on the contour. 48 Number of Bits of Quantization L Fig. 5.7 Fin a l isopreference contours and contours of constant b i t rate i n the r = 1.375 plane. The scale value s or b i t rate R associated with each contour i s shown on the contour. 49 Number of Quantization Bits L F i g . 5-8 F i n a l isopreference contours and contours of constant b i t rate i n the r = 1.65 plane. The scale value s or b i t rate R associated with each contour i s shown on the contour. 50 / 2 3 4 5 6 Number of Bits of Quantization L F i g . 5.9 F i n a l isopreference contours and contours of constant b i t rate i n the r ='2.5 plane. The scale value s or bi t rate R associated with each contour i s shown on the contour. 51 / a 3 4 Ratio of Sampling Frequency to Nyquist Rate r F i g . 5.10 F i n a l isopreference contours i n the L = 4 plane. The scale value, s associated with each contour i s shown on the contour. Ratio of Sampling Frequency to Nyquist Rate r F i g . 5.11 F i n a l isopreference contours i n the W' = 2.12 KHz plane. The scale value s associated with each contour i s shown on the contour. Fig. 5.12 An isopreference surface. Contours of constant L, W and r are shown. 53 i s reached at a smaller value of L. This results because the quantization noise, already made small by a large r, does not require as large a value of L to reduce i t to a point beyond which the l i s t e n e r i s sensitive only to the loss of naturalness due to lowpass f i l t e r i n g . I f W i s increased along a l i n e of constant L, a region i s reached i n which the quality i s primarily l i m i t e d by quantization noise. The larger the value of r i n th i s region, the greater i s the dependence of quality on W, since a small increase i n ¥ results i n a large increase i n sampling frequency when r i s large. For reasons given i n Section 2.5, quantization noise decreases as r increases. The effects of increasing r are also apparent i n Figures '5.10 and 5.11. For example, i n the upper l e f t portion of Figure •5.10, a much larger increase i n ¥ i s required to y i e l d a fixed increase i n scale value than i s required i n the lower right region. Similar comments apply to Figure 5.11. 5.1.3 Minimum B i t Rate Loci Also shown i n Figures 5-6 to 5-9 are points on each contour for which the b i t rate R =' 2r¥L i s a minimum for a fixed value of r. The locus of these point of minimum b i t rate was found i n each case to be a curve defined by the equation ¥ = a ( r ) 2 ^ ^ r ^ . In Figure 5-13, the parameters a(r) and b(r) are plotted as functions of r. . The equations for a(r) and b(r) were found to be closely approximated as follows. "r r < 1. 7 1.7 r>1.7 a (r) (5.D j-.23r+.57 r<1.7 Mr) = .175 r £ 1 . 7 54 It follows that the equation of the locus of minimum b i t rate i n a plane of constant r i s (5.2) 1.0 1.5 2.0 2.5 3 JO Ratio of Sampling Frequency to Nyquist Rate r=fs/2W Fig. 5-13 The var i a t i o n vs r i n the parameters a(r) and b(r) i n the equation W = a(r)2^(r)L. In Figure 5.14, the scale values corresponding to the intersection points of equation (5.2) with the isopreference contours i n each of Figures 5.6 to 5-9 are plotted i n unit normal deviates versus the required number of quantization b i t s and the required bandwidth. For each value of r, the points are f i t t e d well by a straight l i n e , i n dicating that the scale values are normally d i s t r i -2H F i g . 5.14 The scale values corresponding to the ' i n t e r s e c t i o n points of W = a ( r ) 2 M r ) L with i s o p r e f erence contours i n planes of constant r as functions of (a) the required quantiza-t i o n b i t s (b) the required bandwidth. buted over L and ¥. Prom Figure 5.14(a), i t follows that the effect of an increase i n r i s equivalent to a decrease i n L (with the cor-responding change i n W). Such an effect i s suggested by equation (2.12). The parallelism of the l i n e s i n Figure 5.14(a) suggests that an increase i n r has no effect on the s e n s i t i v i t y of the scale value to changes i n L whereas the same increase i n r causes the scale value to become more sensitive to changes i n W. Since f = 2rW, a s given increase i n W i s translated into a large increase i n f • for large r. However, unless Wr i s of the same order of magnitude as the bandwidth of the quantization noise (controlled primarily by L) [28,29] , a change i n r w i l l not tend to affect the s e n s i t i v i t y of the scale value to changes i n L. The maximum, scale value attainable for a given b i t rate R i s plotted i n Figure 5.15 for various values of r. For a l l b i t rates R, the optimum value of r i s r = 1.1. This result indicates that, for a fixed b i t rate, the decrease i n quantization noise i n the receiver passband caused by an increase i n r i s not s u f f i c i e n t to j u s t i f y the required decrease i n L and change i n W. In p r a c t i c a l sys-tems however, L i s constrained to be discrete. It i s therefore of interest to see i f the decrease i n scale value caused by the use of a discrete L may be compensated for by an increase i n r. Table 5.1 shows that even when L i s constrained to be discrete, the optimum value of r i s 1.1. Table 5.1 Comparison of Maximum Scale Values Attainable using Discrete and Continuous Values for the Number of Bits of Quantization L. \ ^ \ r 1 1 1.375 1.65 2 .5 Ldis Lcont Ldis Lcont Ldis Lcont Ldis Lcont 10 2.16 2 . 2 1.98 1.98 1.98 1.98 1.84 1.70 20 4.54 4.65 4.38 4.4 4.05 4.1 3-8 3.8 30 6.63 6.7 6.43 6.47 5.9 6.0 5.15 5.55 40 8.08 8 .2 7.7 7.8 7.5 7.5 6.7 7.0 50 9.05 9.10 8.90 8.95 8.66 8.70 8.08 8.15 .6 10 8 -5 7 5 -4-2 -; -points f r =1.375 not \ shown [ r 1.65 r=2.5 DPCM Results (r as shown) AM Results DPCM (r~l.l) from Donaldson and Chan [l6] PCM from Donaldson and Chan [16] 10 20 30 40 50 50 Bit Rate R (Kbps) Fig. 5-15 The maximum attainable scale value for a fixed b i t rate R plotted for various values of r. Also shown are results presented by Donaldson and Chan for DPCM (r = l . l ) and PCM. The points marked by X correspond to maximum scale values for AM. -a Qi 8 CO F i g . y T T i " 1 1 eg— fa) 7 Bandwidth W (KHz) W= 4.2 / /.5 20 25 3.0 3.5 4.0 Ratio of Sampling Frequency to Nyquist Rate r - fs/2W 5.16 Curves of sca l e value versus -(a) bandwidth W (b) "ratio of sampling frequency to Nyquist frequency f o r the s p e c i a l case of L = 1. Also shown are contours of constant b i t r a t e . 59 A special case, known as delta modulation (AM), occurs for L = 1 and r»l. Since the quantizer for such a system i s very simple, AM i s comparatively easy to implement. The data available from the isopreference tests were not s u f f i c i e n t to permit the derivation of isopreference contours i n the L = 1 plane. By using the data from the rating tests (presented i n Appendix II) however, the curves of scale value versus W and r for L = 1 i n Figure 5.16 were obtained. These curves show that for r> 2 . 5 , the quality of the speech output i s not substantially improved by an increase i n r. Also shown i n Figure 5.16 are contours of constant b i t rate. The maximum attainable scale values for given b i t rates are equal to the maxima of these curves. The scale values and parameter values corresponding to these maxima i n both Figure 5.16(a) and Figure 5.16(b) were found and appear i n Table 5 . 2 . It i s seen that the two sets of results agree almost exactly. The average of the two resultant scale' values appears as the AM curve i n Figure 5.16. • A comparison of the DPCM and the AM curves indicates that only for very low b i t rates i s the performance of AM able to match that of PCM or DPCM. Table 5-2 Maximum Scale Values for Fixed Bit Rates Obtained From Figs. 5.16(a) and (b). R P i s . 5.16(a) _ Fig. -).: L6(b) Average r W(KHz) HMAX r W °MAX 10 1.7 2 .95 2.20 1.8 2.78 2.20 2.20 15 2.03 3-69 3.15 2.17 3-45 3-15 3-15 20 2 .5 4.00 3-90 2 .5 4.00 3-85 3.93 25 2.86 .4.38 4.45 2.75 4.54 4 . 3 4.38 Also shown i n Figure 5.16 are PCM and DPCM minimum b i t rate curves obtained by Donaldson and Chan [ l 6 ] . The DPCM results (r = l . l ) are i n close agreement, although the DPCM curve presented here indicates larger scale values than obtained by Donaldson and Chan when the b i t rate i s large. One possible explanation of th i s discrepancy i s that more steps were used here i n the approximation of the feedback co e f f i c i e n t than were used by -Donaldson and Chan. Another i s that the l o c i of minimum b i t rate are not measured as exactly here as i n [l6j since the present work yielded less data i n the plane r = 1.1 than did [l6] . 5•2 Results of the AM Subjective Tests 5.2.1 AM Results and Discussion The results of the AM subjective tests are shown i n Fig. 5.17. The format of the figure follows that used for the DPCM curves. The points plotted at S/N = 60db were obtained by simply lowpassing the input sentence witoout the addition of noise. This was considered permissible since i t was expected that as S/N was increased, the curves would approach asymptotes determined only by the bandwidth. That t h i s i s indeed the case i s apparent i n F i g . 5.17. As the value of W i s increased along a l i n e of constant S/N, a region i s reached i n which the quality i s primarily l i m i t e d by S/N. However, i f ¥ i s increased further a point i s reached at which the quality begins to deceease. This behaviour may be traced to the r e l a -t i v e absence of signal power i n the high frequency portions of the speech spectrum (see F i g . 4.1) and to the s e n s i t i v i t y of human hearing to high frequency noise [38] . Since, as ¥ i s increased, more noise i s added to the higher frequency portion of the spectrum, the scale value decreases. 5.2.2' Extension of AM Results to Angle Modulation As shown i n Section 2.5, the spectrum of the output noise of an FM System for white Gaussian channel noise varies as the square of the audio frequency. For t h i s reason, the results w i l l be extended only to PM for which the output noise spectrum i s f l a t . The signal-to-noise r a t i o obtained experimentally as des-61 Channel Signal-to - noise Ratio (S(N)C - PJN^ fdb) F i g . 5-17 AM i s o p r e f erence contours. The scale value and. standard d e v i a t i o n associated with each contour i s shown next to the reference point (drawn s o l i d ) through which that-contour passes. Also shown are contours of constant channel capa-c i t y f o r DSB-SC (Cj)) and SSB-SC (C5) communication systems. 62 cribed i n Section J>.1 equals the channel signal-to-noise r a t i o of an AM system Q -n ( -) N cAM ~ N W o The equation for (S/N) ^  may be written AM v ^ ' 7cAM v/_w S i m i l a r l y , the equation for (S/N)p^ may be written (|) = 2 / X*(f) + ~ i / X * ( f ) d f ) N PM 7W ( S / N ) c P M -^W ' where ? ,S, A ,S, ( WcPM- 2 W) ( M ) - V M J .—p PM o P M 2 / N r n c r i i c f W m and" (S/N) cp M'= "(P/fl^W) ^ the PM channel signal-to-noise r a t i o . Por pur-poses of comparison, the assumption i s made that (S/N)p^ and (S/N) ^ may be d i r e c t l y associated with the scale value. In order to operate at a common scale value, (S/N) ^  and (S/N) must therefore be equal. For fixed Wcp^ and W, i t i s therefore necessary to adjust the channel power-to-noise ratios (P/N )jyyj and (P/N^)p^ u n t i l they are equal. For low quality telephone applications a value of W - 2W = IAf of the order of 15 KHz i s t y p i c a l , while for high cPM | I max J ^ ' & quality transmission, 75 KHz i s t y p i c a l ^39]. Results for these two cases are plotted. In order to compare the AM and PM systems, i t 2 2 remains to estimate f and to choose a value for c . Published m results indicate that for speech, the probability that the magnitude of the instantaneous input x(t) w i l l exceed c^x 2 i s less than 2.0$ for a peak factor c > 10 [40] . Approximate values of f corresponding to eight bandwidths are tabulated i n Table 5 . 3 - These values were c a l -culated using the power spectrum of speech from French and Steinberg J36J shown i n Figure 4 . 1 . Using the above approximations, and the equation ( § . ) _ c 2 f S ( V ) , S x 1\T ~ 9 1\T cPM ( W CPM" 2 W^ c A M the results shown i n Figures 5.18 and 5-19 were obtained. Table 5-3 Mean Square Bandwidth of Speech W(KHz) f ^(KHz) m 1 . 0 0 . 2 3 2 1 .2 0 . 2 7 2 1 .5 0.316 2 . 0 0 . 3 6 7 2 . 5 0 . 4 2 2 3 . 0 0 . 4 8 3 3 . 5 0 . 5 4 6 4 . 0 0 . 6 3 3 5 . 3 Comparison of DPCM. PCM, AM, DSB-SC, SSB-SC and PM. It may be shown that regardless of the communication system used, there i s a minimum rate R('e) at which information must be trans-mitted to a receiver i n order to specify an analog source to within a mean square error e [25] • .However, for a channel of fixed bandwidth and signal-tc-noise r a t i o , there i s an upper l i m i t imposed on the rate at which information may be transmitted without r e s u l t i n g i n a high probability of transmission errors. This l i m i t i s termed the channel capacity C. For bandlimited white Guassian channels C = W C l o g 2 (1 + P / N Q W c).(bits/second) ( 5 - 3 ) where P i s the average signal power, .NQ/2 i s the noise power density and W i s the channel half-bandwidth. It follows that a necessary condition for transmitting an analog waveform to a receiving point v i a a noisy channel i s that• • R(e)^C ( 5 . 4 ) 6d • 18 J has e modulate / ° ' ^ c-\/w Pi? tTel C a W = « y ?0°"\TS «-d contour. ' v u • . u l o r peak 4tt 66' The d e f i n i t i o n of the rate d i s t o r t i o n function R(e), does not specify the source of the mean square error e. In analog communi-cation systems, the d i s t o r t i o n of the transmitted waveform by channel noise i s the primary cause of error. However, i n transmitting i n f o r -mation from- a discrete source, i t may be shown that the pro b a b i l i t y of occurrence of channel errors may be made a r b i t r a r i l y small provided that the data rate R^  of the discrete source s a t i s f y R(e)^ R^ s< C, The error i n t h i s case originates mainly i n the sampling and d i g i t i -zation process i n the source encoder. It i s therefore of interest to compare the performances of analog and d i g i t a l communication schemes on the basis of required channel capacity. The channel bandwidth ¥ required by a- SSB-SC system i s c equal to the bandwidth ¥ of the message and that required by.a DSB-SC system i s equal to twice ¥. Therefore, for SSB-SC and DSB-SC, (5-3) may be written (assuming that the noise power i s constant over the channel bandwidth) -. CSSB-SC = W l 0 S 2 ( 1 + (5.5) CDSB-SC = ' 2 W l o g 2 ( 1 + d / 2 ) ( s / N ) c ) where (S/N) = P/No¥ i s the channel signal-to-noise r a t i o . These equations have been plotted i n Figure 5.17 for several values of ^SSB-SC a n (^ ^DSB-SC Marked on the isopref erence curves are. the points for which CggB_gQ and OpgB_gQ are minimum for each, scale value. The l o c i of these- points are shown and were used to derive the SSB-SC and DSB-SC curves i n Figure 5.18. • The channel bandwidth required by a PM system i s given approximately by equation ( 2 . 2 3 ) . The required channel capacity for PM communication i s therefore given by . . ' 0 = 2(lAfLax + 2 W ) l o S 2 ( 1 + 2<N>C (-(Af| 67 1 / S v / W v - 2W max This equation was plotted i n Figures 5-18 and 5-19 for Af = 75 KHz and JAfl = 15 KHz and for c =s/20 and c =v/lO. The l o c i of the 1 max points of minimum channel capacity were then obtained and used to derive the P M contours i n Figure 5.20. However, since as ( S / N ) decreases i n a P M system, the approximation 2 N Q W « A made i n the d e r i -vation of (2.25) becomes i n v a l i d . This phenomenon known as "thres-holding" occurs for ( S / N ) X 25 db for |Af I = 75 KHz and ( S / N ) ^ 18 db for 1 Af| = 15 KHz*. For c =v£o, t h i s corresponds to a channel capacity 0= 400 Kbps for |Af| = 75 KHz and ID. SIX C ^ 70 Kbps for |Af| = 15 KHz. Although t h i s appears to invalidate the P M results shown i n Figure 5.20, the asymptotic behaviour of these curves i s s t i l l useful i n estimating the performance of P M as compared to other communication systems which use large channel capacities. The minimum b i t rate curves shown i n Figure 5-15 correspond to the discrete source data rate mentioned e a r l i e r . By l e t t i n g C ^ P C M ' the D P C M required channel capacity, equal R-^ /k, the D P C M curves of minimum channel capacity shown i n Figure 5.18 were drawn. The parameter k i s a measure of the eff i c i e n c y of the code used. A value of k = 1 implies perfect coding i n the sense that negl i g i b l e channel error occurs without the necessity of increasing the channel capacity. The values of k = 5/4 and k=l/2 indicate codes which require channel capacities equal to (4/3)R-^ and 2R-^  respectively, i n order to obtain the required negligible probability of a transmission error. The remaining curve i n Figure 5.20 i s derived from the locus of minimum b i t rate for P C M shown i n Figure 5.15 and i s shown only for perfect coding. From Figure 5.20 i t may be concluded that for low values of * These values were estimated using equation (.7) of Wojnar [41] • 30 40 so so Channel Capacity C (Kbps) •-'69 channel capacity, SSB-SC and DSB-SC outperform DPCM, AM, and PCM i n speech communication. The reason for th i s may be traced to the dis-" t i n c t l y structured quality of the noise created by d i g i t a l systems, as opposed to the randomness of the noise heard i n analog systems. Humans appear* to be more annoyed by noise with strong structure than by random noise* and, i n the region of the curves under consideration, the noise l e v e l s are quite large. As the channel capacity i s increased, the PCM and DPCM systems are permitted to quantize more f i n e l y and sample more often. The fi n e r quantization causes the granular struc-ture of the d i g i t a l noise to be less noticeable. As a r e s u l t , the PCM curve gradually approaches the DSB-SC curve, u n t i l for very high quality speech communications, PCM becomes more e f f i c i e n t than DSB-SC (for 100$ e f f i c i e n t coding). The'fact that DPCM i s better than PCM i s . a result of the increased redundancy reduction c a p a b i l i t i e s (resul-t i n g from an improved prediction) afforded by the f i n e r quantization and higher sampling frequency. In effect R-^  approaches R(s) more closely. The results i n Figure 5.20 also indicate that for large channel capacities, DPCM outperforms PM for speech communication. It i s interesting to compare these results with the theoret-i c a l results presented by Goblick [24]'. Goblick concludes that unless the channel signal-to-noise r a t i o i s substantial and, i n the case of d i g i t a l communications, the source d i g i t i z a t i o n e f f i c i e n t , the modu-l a t i o n systems which expand bandwidth cannot be used to good advantage. D i g i t a l and angle modulation systems are such systems. I t may be seen that the conclusions reached here agree with those of Goblick. 5.4 T r a n s i t i v i t y Checks In Figures 5.6, 5.8, and 5.17 are shown points marked T l , T2, T3 and T4. AM reference points 3, 4, and 5 were used i n isopre-* Similar responses have been reported for picture quantization. See for example [22] and J23] • 70 ference tests to obtain the equal preference DPCM points T l , T2 and T3, and DPCM reference point 2 was used to obtain T4. The scale value corresponding to each of these reference points i s shown next to the obtained point. Prom these points, i t appears that the results obtained for T3 and T4 are not as consistent as one might expect. One of the fac-tors contributing to the inconsistency may be the inaccuracies caused by terminating (at 0 and 10) the t a i l s of the d i s t r i b u t i o n of scale values curve. Another factor i s the difference i n types of noise appearing i n the two systems, a difference which i s most apparent for the lower scale values. Although t h i s l i m i t s to some extent the v a l i -d i t y of the comparison of the DSB-SC and DPCM res u l t s , i t does not necessarily have any bearing on results obtained by comparing one set of curves. 5.5 Concluding Remarks The results obtained here indicate that for DPCM the sampling frequency should be made as close to the Nyquist rate as possible without causing large a l i a s i n g errors. However, r e s t r i c t i o n (3) i n -Section 4.2.1 (which l i m i t s the amplitude of the input to the quan-t i z e r ) may not be a p r a c t i c a l one with the result that slope overload noise [ l 4 l becomes a major problem. Since t h i s form of noise i s very dependent on the sampling frequency, i t i s reasonable to expect that an increase i n sampling frequency may be very desirable. A possible approach to th i s problem would be to use some form of adaptive gain at the input. 71 APPENDIX I Feedback Coefficient Optimization 2 •The mean square.error e.(t) at the output of the predictor shown i n Fig. A.1.1 i s given by e 2 ( t ) = (x - x ) 2 = [ x - |_] «kx(t-kT)] (A.1.1) This equation i s minimized when the oc^ 's are solutions to the follow-ing set of l i n e a r equations [ 27J S <x.0 . . (A.1.2) .where 0, = R (kT)/R (o) and R (T) i s the autocorrelation function XV -A. JC of x ( t ) . The optimum o^'s may be written a k •(A.1.3) Fig. A.1.1 An N order l i n e a r predictor. 72 where |p| i-s. the determinant of the matrix of the coefficients of the oc^ 's on the right hand side of (A. 1.2) and P^ i s the determin-th' ant of P with i t s k column replaced by the column vector ( 0 - ^ , 0 2 , . . . , 0j j ) . The resultant mean square error i s given by e 2 n ( t ) t e 2 ( t ) / x 2 ( t ) = 1 - ^ cc 0 (A.1.4) i = l The optimum a-^ 's are plotted i n Pig. A.1.2, for N = 1, 2, 3 for the part i c u l a r case of speech of bandwidth greater than 1.5 KH^• Por N> 1 and high sampling frequencies, the evaluation of the optimum o^'s becomes very d i f f i c u l t , since |P| and |P^| approach zero r e s u l t i n g i n a r a t i o of two very small quantities. Since, for x(t) wide-sense stationary, R (T) = R (-T ) , 0 V may be approximated by X x a polynomial of the form 0 k = 1 - & 1 (kT) 2 - a 2 ( k T ) 4 - . . . . - a j j ^ C k T ) 2 ^ " 1 5 . " Using t h i s approximation ( A . l . l ) may be written e 2 / x 2 = f Q ( a ) + ^ ( ^ a ^ 2 + ....+ f N _ 1 ( a ) a N _ 1 T 2 ( N - l ) . where "a = ( , oc^) , and f.(ct) i s a function representing th _>. » the dependence of the i coeffi c i e n t on ct*. By choosing a to be a solution of f ± ( a ) = 0 (I = 1,2, ,N)' (A.1.5) e 2 / x 2 i s made equal to zero to an N - l " ^ order approximation. The solutions to A.1.5 are represented by the asymptotes of the curves i n Pig. A.1.2 as T->o(f - * o b ) . s The discrete values (a^) of used i n the previous sample feedback (N•= l ) experiments are shown i n Pig. 4.2. A measure of the 73 effect of using ct^  may be' obtained by defining the function 2 / 2 2 r.. = e_ / e where e i s the mean square error obtained by using a a A ., . ^ large value of r indicates a bad choice of a n . The maximum 1 & g 1 values of r , which occur for the values of time delay T at which g changes values, are tabulated i n Table A. 1.1. For f & 15KHz(T > .067ms), i t may be seen that the deterioration i n per-s formance i s less than 0.1 db. Table A . l Values of r = e. a 7 eQ corresponding to points of maximum discrepancy between a-, and i t s approximation a.. (Bandwidth W2 1.5KHg) x x f (KHz) o T(ms) * i " l r g r (db) g 2.56 • 39 • 38 .33 1.0029* .001 2.56 .39 .38 .45 1.057* .025 3-51 .29 .534 .45 1.0099 .043 3-51 .29 .534 .60 1.0061 .026 4.3 .233 .674 .60 1.0100 .043 4.3 .233 .674 .70 1.0012 .005 5.0 .2 .754 .70 1.0068 .029 5.0 .2 .754 .80 1.0049 .021 6.9 .145 .864 .80 1.0162 .070 6.9 .145 .864 .90 1.00512 .022 10.0 .1 .936 .90 1.0105 .045 10.0 .1 .936 .95 1.0016 .007 15.0 .075 .962 .95 1.0013 .006 33.0 .0303 .994 .95 1.162 .652 However, for f > 15KHz(T£ 0.067 ms), s t a b i l i t y considerations die-tated that cx^  not be too close to unity. Therefore, <x^  was limi t e d to 0.95. As a r e s u l t , as f i s increased from 15KHz, r also i n -s g creases. The maximum frequency considered i n the experiments was 33KHz. The corresponding value of r i s included i n Table A.1.1. g Similar results may be derived for the 2 and 3 sample feedback cases, although considerable computation i s required. These values were calculated for W = l.OKH^ since for f X 3-3KH<5 the autocorrelation function for W = 1.5KHz does not apply. \ / / / A. 1.2 Optimum p r e d i c t o r c o e f f i c i e n t s OCJ_.J. The s u b s c r i p t i r e f e r s to 1, 2, or 3 i n t e r v a l s of time delay and s u b s c r i p t j r e f e r s to the order of the p r e d i c t o r . APPENDIX I I Rating Test Data A.2.1 Results of DPCM P i l o t Rating Tests 75 Parameters Sample Mean Std. Dev. L W(KHz) r 4. 1 . 0 1 1.1 2 . 2 1 .21 5 3-17 1 .25 5 .94 1 .29 3 4 . 2 1.1 5 . 3 7 1 .59 5 3-17 3 . 0 7 . 6 8 1 . 3 0 3 2 . 6 3 1.5 4-92 1 .61 5 2 . 6 3 2.4 7.82 .97 5 2 . 6 3 1.5 7 . 9 7 1.06 2 1 .01 2-4 .85 .60 1 6 . 3 .1.25 2 . 4 5 1.26 1 2 . 6 3 2 . 4 2 . 8 5 .94 6 2 . 6 3 1.25 7 .35 1 . 2 0 3 2.12 1 .25 4 . 4 3 1 . 5 0 2 6 . 3 2 .4 7.12 1 .66 6 1 . 0 1 1.5 2 . 5 1.13 6 4 . 2 1 .25 8 . 3 5 1 .13 '2 2 . 6 3 3-0 6 . 3 5 1 . 3 0 4 2.12 1.1 4 . 3 7 1 .29 2 2 . 6 3 1 .9 4 . 6 8 1 .47 2 4 . 2 1 .9 5 . 3 3 1 . 5 8 1 1 . 0 1 3 . 0 .85 .55 4 2.12 2 . 4 6.18 1 .45 6 1 .55 3 . 0 5 . 0 3 1 .43 1 1 .01 1 .25 .65 . 6 3 3 2 . 6 3 1.1 3 . 7 8 1 . 2 0 2 4 . 2 3 . 0 7.28 1.61 5 1 . 0 1 1 .9 2.80 1 . 3 8 2 1 . 0 1 1.5 . 9 3 .75 6 2.12 2 . 4 6 . 4 3 1 .57 5 1 .01 3 . 0 3-15 1.28 3 1 . 0 1 3 . 0 2.70 .92 2 3.17 2.4 5.72 1 .56 5 1 .55 2.4 4.62 1.28 1 3-17 1 .25 1.89 1 .34 5 2.12 1 .25 6 . 3 8 1 .34 5 3-17 1 .25 8.27 .87 3 6 . 3 1 .25 7.08 1 .53 3 2 . 6 3 2 . 4 7 . 2 2 1 .34 . 4 3-17 1.1 6.75 1 .43 6 6 . 3 1.1 8.60 .91 6 3.17 1.5 7.90 1.12 1 1.55 1.5 .62 .72 4 3.17 1.5 7 .53 1.09 3 2.12 3-0 6 . 0 5 1 .63 3 1-55 1.1 2.13 1.06 6 2.12 1.1 5 . 8 5 1.71 Parameters Sample Mean Std. Dev. L W(KHz) r 6 2.12 1.1 8.15 1.20 6 1.01 1.1 . 2.02 .94 4 2.63 3.0 8.15 1.17 5 1.01 1.25 2.40 1.26 3 1.55 1.5 2.60 1.08 1 2.12 1.25 .75 1.02 1 2.12 1.9 1.70 1-33 5 2.12 3-0 6.95 .1.50 2 2.12 1.1 2.30 1.24 1 3.17 1.9 2.48 1.33 2 2.63 .1.25 2.63 1.32 1 1.55 1.1 .43 1.62 6 2.12 1.5 6.78 1.34 4 3-17 2.4 8.58 ' • 98 3 1.01 1.9 2.18 1.08 1 4.2 1.5 2.35 1.00 2 1.01 1.1 .73 .67 1 •3-17 3-0 3-72 1.10 4 1.55 3.0 4.78 1.42 2 2.12 . 1-5 4.12 1.26 2 2.12 2.4 4.97 1.10 3 1.55 2.4 3-87 1.09 5 1.55 1.1 3.62 1.23 1 2.63 1.5 1.93 1 .15 5 4.2 1.5 8.70 1.37 4 2.12 1.5 6,78 .85 4 1.01 1.5 2.75 1.05 4 1.01 2.4 2.67 1.08 4 1.55. 1.9 4.68 1.36 2 3.17 1.1 3.10 1.26 2 6.3 1.5 4.92 1.60 6 2.63 1.9 7.85 1 .15 1 4.2 2.4 4.40' 1.43 3 4.2 3.7 7.15 1.28 1 6.3 1.9 4.10 1.45 2 3-17 1.5 3.68 .98 1 1.55 2.4 .98 .94 4 1.55 1.25 3.48 1.46 6 1.01 2.4 2.95 1.66 4 4.2 1.25 7.82 .95 2 1.55 1.25 1.50 .68 1 2.12 3-0 1.73 .84 3 3.17 3-0 8.15 1.34 4 6.3 1.5 8.78 1.04 5 2.63 1;1 6.98 1.03 Parameters Sample Mean Std. Dev. L W(KHz) V 3 4 . 2 2 . 4 7 . 7 3 1 .24 1 1 .01 1 .9 . 3 3 .42 2 6 . 3 . 1.1 3-95 1 .51 3 2.12 1 .9 5 . 0 5 1 .51 3 4 . 2 1.5 6.12 1 .58 5 3-17 1 .9 8 . 7 3 .96 6 1 .55 1 .9 3-85 1 .25 3 1 . 0 1 1 .25 1 . 5 0 • 97 4 6 . 3 1 .1 7 . 5 8 1 .34 5 2.12 1 .9 6 . 5 0 1 .24 2 3.17 3 . 7 7 . 3 2 1 .21 3 3-17 1 . 9 7 . 1 0 1 . 0 9 5 4 . 2 1.1 8 . 2 7 1.11 5 1.55 1.5 3 . 8 8 1 .50 2 4 . 2 1 .25 • 3 . 6 3 1 .27 6 1 .55 1 .25 3 . 9 5 1 .55 2 1 .55 1 .9 1 . 9 3 .91 1 4 . 2 3 . 7 3 . 8 8 1 .32 4 4 . 2 1 .9 8 . 5 7 .96 1 2 . 6 3 1.1 1.17 .97-3 6 . 3 1 .9 7 . 5 5 1 .33 1 4 . 2 1 .1 1 . 5 3 . 9 0 2 1 .55 3-0 2 . 8 3 1 . 2 0 4 2 . 6 3 1 .25 6 . 5 3 1 .31 4 2 . 6 3 1 .9 8 . 2 5 .97 5 6 . 3 1 .25 9.15 .69 Table A.2.2 DPCM Reference Point Rating Tests Parameters Sample Mean Std. Dev. Parameters Sample Mean Std. Dev. a* li W(KHz) r L W(KHz) r 3 4 2.12 1.375 4.16 1.31 1 4 2.12 1.375 4.14 1.35 2 4 2.12 1.375 4.29 1.34 1 1 3-17 4.0 3-35 1.50 2 3 2.63 1.375 4.55 1.45 1 4 2.63 1.65 6.91 1.71 2 4 2.63 1.65 7.11 1.54 1 3 2.12 1.21 4.06 1.42 2 5 3-17 1.65 8.175 1.27 1 5 2.63 1.375 7.45 1.58 2 2 1.55 1.1 1.09 0.93 1 3 2.63 1.375 4 . 8 8 1.48 2 5 2.63 1.375 7.81 1.62 1 4 2.12 1.21 3-84 1.42 2 3 2.12 1.1 3-875 1.31 1 1 3-17 3.5 2.675 1.27 2 3 2.12 1.21 • 4.275 1.36 1 2 1.55 1.1 0.81 0.63 2 4 2.12 1.21 3.925 1.44 1 5 3-17 1.65 8.88 1.63 1 1 3.17 2.5 2.46 1.02 1 3 2.12 1.1 3.36 1 . 3 0 1 1 3-17 3.0 2.48 1.08 N =• number of samples of feedback. 77 Table A.2. 3 AM P i l o t • Parameters Mean Std. Dev. S/N(db L W(KBz; r 21.1 4.2 7-05 1.09 20.1 1.01 2.5 1.46 DPCM 5 2.63 1. 375 8.48 1.06 21.5 2.63 6.85 1.39 DPCM 6 3-17 1. 375 9-05 .81 DPCM 2 '3.17 1. 375 4.18 1.35 DPCM 4 4.2 . 1. 1 8.13 1.19 11.0 1.01 1.63 .97 DPCM 2 3-17 2. 5 7.08 1 .23 DPCM 2 4.2 1. 65 5.18 1.28 DPCM 3 2.63 2. 5 8.45 1.27 16.3 2.63 5-95 1.16 34.2 6.3 9.13 .69 DPCM 1 3-17 1. 1 1.5 .93 DPCM 3 2.12 1. 1 4-38 1.55 DPCM 4 2.63 1. 65 8.. 43 1.24 Table A.2.4 Para meters Mean Std. , S/N(db; L W(KBz) r Dev. 9 . 5 2.12 3-34 1 .59 DPCM 7 2.12 1 .65 5 .95 1 .96 7 . 0 1 . 0 1 1 .69 1 .27 DPCM 6 3.17 1 .375 7.72 1 . 6 3 DPCM 3 2.12 1.1 3-31 1 .37 60 .0* 1 .55 4 . 4 1 1 .73 - 3 - 0 4 . 2 1.75 1.14 18 .2 3.17 6 . 1 1 . 4 8 DPCM 4 2 . 6 3 1 .65 6 . 8 3 1 .85 2 3 - 0 6 . 3 6 . 6 4 1 .56 DPCM 2 4 . 2 1 .65 4 - 3 0 1 .75 3 3 - 0 6 . 3 8 . 6 6 .91 2 1 . 1 4 . 2 6.72 1.42 60 .0* 1 . 0 2 . 5 1 . 3 0 3-0 1 .55 1 . 6 3 1.11 3 0 . 8 4 . 2 8.08 1 .23 7 . 0 1.55 2 . 3 3 1 .76 1 6 . 3 2 . 6 3 5-58 1 .44 1 9 - 0 2 . 6 3 . 4 - 3 8 1 .52 1 4 - 0 2.12 6 . 9 8 1 .29 Parameters Mean Std. S/N(db; L W(KHz) r Dev. 17.6 1.55 4 .13 1.81 7.03 1.01 1.45 1.36 DPCM 5 2.12 1.1 6.8 1.73 19.1 2.63 6.75 1.60 DPCM 3 2.63 1.375 6.08 1.17 23-3 6.3 7.48 1.4 18.2 3.17 6.75 1.18 9 .13 2.12 4.2 1.20 DPCM 7 2.12 1.65 7.05 1.97 DPCM 2 1.55 1.1 1.05 .81 DPCM 5 3-17 1.65 9.48 .80 DPCM 1 3-17 1.65 2.05 1.09 DPCM 1 2.63 2.5 2.9 1.20 21.7 3.17 7.43 1.04 14.6 2.12 5.5 1.48 11.4 1.55 3.63 1 .32 Point Rating Tests Parameters. Mean Std. S/N(db) L W(KFJz) r Dev. 27.0 3.17 3.27 1.44 17.8 1.55 4-52 1.71 10.0 6.-3 4.52 1.71 24.6 3.17 7 .30 1.33 DPCM 5 3-17 1.65 8.88 1.25 60.0* 2.63 7 .03 1.81 23-0 3-17 6.89 1.40 DPCM 3 2 ,63 1.375 4.72 1.73 60.0"y- 4.2 9.27 .81 60.0* 2.12 4 . 6 6 1.82 31.75 1.55 3.81 1.46 24.8 4.2 7.53 1.82 DPCM 2 1.55 1.1 1.22 1.24 60. 0* 3-17 8.73 1.33 27-0 4.2 7.42 1.19 3-0 1.23 1.05 .73 34.8 4.2 8.56 1.27 60.0* 1 .23 3.25 1.16 DPCM 1 3-17 1.1 1.08 1.02 21.8 2.63 6.45 1.35 * The value of 60 db i n these tables corresponds to zero noise added to the speech sample. 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