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Mechanical voice synthesiser Kugel, Harish; Miller, Tristan Apr 4, 2011

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Mechanical Voice Synthesiser  Harish Kugel Tristan Miller Project Sponsors: Dr. Mark Halpern Dr. Chris Waltham Project # 1118 Applied Science 459 Engineering Physics Project Laboratory The University of British Columbia April 4, 2011 1  Executive Summary The purpose of the project was to design and build a well understood mechanical voice simulator of the human vocal tract. In essence, various vowels and consonants were to be created using the device by adjusting its dimensions. Once completed, this model was to be used as an instructional instrument to assist in the understanding of the theory behind human voice production. Finally, if time permitted, the model was to be made automatically controlled. The first part of the project involved simplifying the human vocal tract as a double Helmholtz resonator, modeling it as a double spring-mass system and developing a theory to determine the resonating frequencies of the device. To verify the theory, prototypes with fixed dimensions were built and tested to compare the measured resonant frequencies with the predicted frequencies. The final dynamic device was then built and a mapping of the resonances as a function of the significant dimensions was constructed. By matching these resonant frequencies with the fundamental vowel frequencies given by the IPA, the device was able to produce most of the English vowel sounds. Although this was successful, the theory was unable to predict the frequencies emitted by the device, given a set of dimensions. For future development of this project, it is recommended that the theory be revisited in a less generalized manner to accurately predict the output of the dynamic double Helmholtz resonator. Additionally, the project could be expanded upon to include consonants by adding another resonant chamber for the nasal cavity.  2  Table of Contents Executive Summary  .  .  .  .  .  .  .  .  .  2  List of Figures .  .  .  .  .  .  .  .  .  .  4  List of Tables  .  .  .  .  .  .  .  .  .  .  4  1. Introduction .  .  .  .  .  .  .  .  .  .  5  2. Discussion  .  .  .  .  .  .  .  .  .  .  7  3. Conclusions .  .  .  .  .  .  .  .  .  .  15  4. Project Deliverables .  .  .  .  .  .  .  .  .  16  5. Recommendations  .  .  .  .  .  .  .  .  .  18  Appendix A  .  .  .  .  .  .  .  .  .  .  19  Appendix B  .  .  .  .  .  .  .  .  .  .  23  Appendix C  .  .  .  .  .  .  .  .  .  .  24  References  .  .  .  .  .  .  .  .  .  .  30  3  List of Figures Figure 1  Schematic of Double Helmholtz  .  .  .  .  .  7  Figure 2  Frequency Spectrum of Wine Bottle .  .  .  .  .  9  Figure 3  Final Design Components  .  .  .  .  .  11  Figure 4  Characteristic Waterfall Praat Plot  .  .  .  .  .  11  Figure 5  Characteristic Plot of Formant Behaviour  .  .  .  .  12  Figure 6  Plot of Theoretical Formant Behaviour  .  .  .  .  13  Figure 7  Comparison of the Real Pronunciation and the MVS Imitation for ‘e’  14  .  List of Tables Table 1  IPA Vowel Formant Centers. .  .  .  .  .  .  10  Table 2  Breakup of Project Expenses. .  .  .  .  .  .  16  4  1. Introduction 1.1 Background and significance of the project The purpose of this report is to detail how time and resources were used in meeting the goals of the project in question. Furthermore, this report seeks to discuss the results of the project and to give recommendations to either reach or exceed these goals in the future. The objective for the project, given by Mark Halpern and Chris Waltham of the Physics and Astronomy Departments at UBC, was to design and manufacture a mechanical device that is capable of producing English vowel and consonant sounds. Once completed, the final device was to be used as a physics demo for courses on Acoustics. While there have been many other devices which meet these specifications made elsewhere, none have successfully been made at UBC. One such existing technology is a speech production mechanism currently being researched at Japan’s Kagawa University. This device creates Japanese vowels and consonants by imitating the precise configurations of the mouth when a person speaks. The design has a stronger focus on replicating the human vocal tract than on creating a mechanical substitute through numerical predictions. A second existing mechanism uses fixed hollow plastic tubes to mimic the vocal tract. The initial sound is produced with a duck call which then travels through moulded plastic to form a vowel sound. The design is not tuneable so each vowel sound has a single corresponding plastic model. The experiment performed last year also had the same objectives. However, as mentioned above, it resulted in failure. Therefore, in the pursuit of a working mechanism, the project was revisited. For individuals who are not experts in the field of acoustics, basic background in frequency spectra, resonators and Phonetics would be very helpful in understanding the theory, design and results of the project.  1.2 Statement of the Problem / Project Objectives The project objectives are as follows: to produce vowel sounds using a mechanical model of human speech production, to produce consonant sounds using a mechanical model of human speech production and to make the model automatically controlled, if time permits.  1.3 Scope and limitations To meet the objectives stated above, it is necessary to be able to calculate the response of an acoustical system so as to reliably design such a system. To do so, a simplified model of an acoustical system was used, called Lumped Element Analysis. One might endeavour to solve the wave equation exactly for such a system but that is out of the scope of this project and report. As a consequence, some error will be introduced into our results. Furthermore, the project scope has been narrowed to only include vowels that require continuous air flow. Vowels and/or consonants which require stoppages in the flow of air will not be pursued during the project or discussed in this report. Also, because of time  5  limitations, the project objectives may be simplified to facilitate a shorter time frame, as mentioned above  1.4 Organization This report consists of four main sections. The Discussion section which discusses the theory, method and results of our project, the Conclusions section which includes the final inferences from the results, the Project Deliverables section which describes the financial details, ongoing issues and products of the project and the Recommendations section which suggests how the project may be continued in the future.  6  2. Discussion 2.1 Theory Each English vowel sound is composed of two fundamental frequencies ranging from 320Hz to 2500Hz. One way to obtain these frequencies is to use coupled resonant cavities which filter out all but two frequencies. These coupled cavities are known as Helmholtz Resonators and can be mathematically modeled by an LC circuit or a double spring-mass system (Figure 1). Theories for both the electrical and mechanical analogue were developed but the spring-mass model was primarily used and will be focused on in this report. The theory for the electrical analogue is included in Appendix A.  Neck  Cavity  Figure 1 – LC circuit and Spring-Mass approximation of the double Helmholtz. The Inductor/Mass corresponds to the neck and the Capacitor/Spring corresponds to the cavity.  The resonating frequencies of the spring-mass system correspond to the filtering frequencies of the device. The effective spring and mass constants are determined from the physical dimensions of the Helmholtz cavities by: ‫=ܭ‬  ߛܲܽଶ ܸ  ‫ ݎߨ = ܯ‬ଶ ݈‫݌‬  Where a is the cross sectional area of the neck, V is the volume in the cavity and M is the physical mass of air in the neck. Therefore, by changing the dimensions of the cavities the resulting filtering frequencies can be tuned. These frequencies are calculated simply from the two equations of motion governing the double spring-mass system: 7  ݉ଵ ‫ݔ‬ሷ ଵ + ሺ݇ଵ + ݇ଶ ሻ‫ݔ‬ଵ − ݇ଶ ‫ݔ‬ଶ = 0 ݉ଶ ‫ݔ‬ሷ ଶ + ݇ଶ ‫ݔ‬ଶ − ݇ଶ ‫ݔ‬ଵ = 0  Combining these two equations together in matrix form gives: ൤  ݉ଵ 0  0 ‫ݔ‬ሷ ଵ ݇ + ݇ଶ ൨൤ ൨ + ൤ ଵ ݉ଶ ‫ݔ‬ሷ ଶ −݇ଶ  −݇ଶ ‫ݔ‬ଵ 0 ൨ቂ ቃ = ቂ ቃ ݇ଶ ‫ݔ‬ଶ 0  Assuming there is a harmonic solution for x of the form:  ቈ൤  ݉ଵ 0  ‫ݔ‬ሺ‫ݐ‬ሻ = ܺ݁ ௦௧  0 ଶ ݇ + ݇ଶ ൨‫ ݏ‬+ ൤ ଵ ݉ଶ −݇ଶ  −݇ଶ ܺଵ ௦௧ 0 ൨቉ ൤ ൨ ݁ = ቂ ቃ ܺଶ ݇ଶ 0  A trivial solution exists for X=0, therefore in order for a non-trivial solution to exist the determinant of the left hand side must be zero. det ቈ൤  ݉ଵ 0  0 ଶ ݇ + ݇ଶ ൨‫ ݏ‬+ ൤ ଵ ݉ଵ −݇ଶ  −݇ଶ 0 ൨቉ = ቂ ቃ ݇ଶ 0  This gives a quadratic equation with roots of s2. This dummy value of s is related to the resonant frequency by: ‫ݏ‬ଵ ଶ = −‫ݓ‬ଵ ଶ  ‫ݏ‬ଶ ଶ = −‫ݓ‬ଶ ଶ One assumption of this theory is that the air pressure instantly changes from inside the neck to inside the cavity. In order to compensate for this and approximate the actual pressure gradient that is present, neck length corrections were added which are a function of the neck radius. Another way to consider this is that the mass within the neck is vibrating back and forth and so has an effective length that is actually longer than the neck.  2.2 Method Once the theory had been developed the next step was to verify it. As an initial investigation, a single Helmholtz (one spring one mass) was tested. This entailed blowing over a wine bottle and recording the resonant frequency using the program Audacity and comparing it with the predicted frequency. Figure 2 shows a result of this measurement with the wine bottle half full of water. For all the single Helmholtz tests the theory was within 10% of the actual resonance.  8  Figure 2 – Frequency spectrum of a wine bottle half full with water. The plot was produced using the program Audacity.  The next stage was testing the theory for a double Helmholtz. This was done by building three prototypes with fixed specific dimensions and comparing the output frequencies with the predicted ones. Since the device acted as a filter filter, a broad spectrum of frequencies requencies needed to be put in to ensure that the resonant frequencies were included. To provide this wid wide e spectrum the device was driven using a duck call as source. The first two prototypes types were found to be within 88% of the expected frequencies quencies but the third was off by up to 50%.. This was most likely due to the minute size of the third model model.. Since the cavities ca were so small the air inside was insufficient to act as a spring and so the theory began to break down. The next step was to build a device with dynamic dimensions that could output a range of frequencies. In order to simplify the design it was dete determined that all the formant frequencies of the English vowel sounds in Table 1 could be produced by changing only the lengths of the large cavities. The final device was then created with all fixed dimensions except for the cavity lengths.  9  Table 1 – IPA vowel formant centers  2.3 Final Device The final dynamic device, named the Mechanical Voice Synthesizer (MVS), is shown in Figure 3. It operated by changing the cavity lengths via moving the effective masses (diaphragms) through the device. These diaphragms are shifted by using magnets to pull them along the apparatus. The sound input is created by forcing a continuous flow of air through the duck call at the entrance of the device.  Figure 3 – Picture of the components of the Mechanical Voice Synthesizer.  10  2.4 Results In order to test the final device the programs Audacity and Praat were utilized and the data was recorded using a laptop’s internal microphone. Audacity was used to record the frequency spectrum while Praat assisted in determining the resulting formants. Figure 4 shows a waterfall plot from Praat. The areas with concentrated ‘waves’ are the formants of the frequency spectrum. It was found that the precision of the cursor to determine the frequency was +/- 50Hz.  Figure 4 – Characteristic image of a waterfall plot from the program Praat.  To provide a general understanding of how the device performed data was collected by fixing the first cavity length and moving the other in 1cm intervals and recording the output frequency then increasing the first cavity by 1cm and repeating. A characteristic plot of the resulting data is shown in Figure 5 and the data in its entirety is in Appendix C. For the three formants listed, the general trend was decreasing frequency with increasing length. This can be explained by the larger cavity length corresponding to longer standing waves and thus smaller frequencies. Another trend was that the formants tended to converge as the cavity increased. Eventually the frequencies were considered the same since they were indistinguishable in Praat. The lower unchanging frequency can be attributed to pipe resonance, i.e. a frequency corresponding to a standing wave along the entire length of the pipe. This was why the frequency remained constant with changing cavity lengths. For the purpose of this report frequencies above 3500Hz were not considered since the maximum vowel frequency was only 2500Hz.  11  Characteristic Plot of Formant Behaviour 4000 3500  Frequency (Hz)  3000 2500 Formant 1  2000  Formant 2  1500  Formant 3  1000  Pipe Resonance 500 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Pipe 1 Length (cm)  Figure 5 - Plot of the MVS output frequencies with the first cavity length fixed at 3cm and the second ranging from 1cm to 13cm.  For comparison, Figure 6 shows the theoretical output frequencies. There were only two formants in the theoretical model because the simplified spring-mass analogue only accounted for the two lowest resonant frequencies, whereas in reality there are additional higher frequencies. The actual magnitude of the measured and theoretical frequencies differed by up to 900Hz for the higher frequencies and 600Hz for the lower frequencies. This was most likely due to an oversimplification of the system with Lumped Parameter Analysis. Another source of error could be the vibration of the diaphragms causing inaccurate cavity lengths and additional low frequency resonances. Additionally, inadequate sealing around the diaphragms caused a loss of pressure within the cavities which could have changed the effective spring constants.  12  Plot of Theoretical Formant Behaviour 1200  Frequency (Hz)  1000 800 600 Formant 1 400  Formant 2  200 0  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14  Pipe 1 Length (cm)  Figure 6 - Plot of the theoretical MVS output frequencies with the first cavity length fixed at 3cm and the second ranging from 1cm to 13cm.  After the mapping of the frequency output of the MVS was completed, it was determined which set of cavity lengths corresponded to vowels. This was done by finding orientations with formants matching the dominant frequencies of the specific vowel sound and audibly comparing the sound with the actual vowel. Figure 7 shows a comparison between the Praat plots of the MVS and a real pronunciation of the vowel ‘e’ (in IPA standard). For this vowel the dominant frequency was 2300Hz and the minor frequency was 500Hz. Evidently, the MVS was able to output frequencies close to the desired values. This was true for each of the vowels where the recorded formants from the MVS were within 10% of the dominant frequencies.  13  Comparison of the Real Pronunciation and the MVS Imitation for ‘e’  Figure 7 - (Left) Waterfall plot of real pronunciation of 'e'. (Right) Waterfall plot of MVS output for 'e'.  The audible sound from the MVS was also similar to human pronounced vowel sounds. However, there was always an undertone of the vowel ‘u’ which can be attributed by the pipe resonance explained earlier. This resonance was around 350Hz and the dominant formant for ‘u’ is 320Hz. Due to this consistent underlying low frequency, the sound ‘u’ was always present.  14  3. Conclusions The goal was to create a device that could mimic the human vocal tract and produce vowel sounds. The first step towards this objective was to develop a theory that could predict the resonant frequencies of a single Helmholtz and then a double Helmholtz based on the dimensions of the apparatus. This theory entailed using lumped parameter analysis to model the setup as a spring-mass system. Using wine bottles as a single Helmholtz, the theory matched the resonant frequencies to within 8%. After building double Helmholtz prototypes and adding end corrections to the theory, it was able to predict the resonant frequencies of the prototypes to within 10%. The theory was then used to construct the final device (Mechanical Voice Synthesizer) where the range of vowel frequencies could be produced by adjusting only the lengths of the two cavities. While the general trends of the frequency response with cavity length matched the theory, it was not able to accurately predict the magnitude of the resonant frequencies as it was off by 20-300%. This was most likely due to oversimplification of the acoustical system. A mapping of the output frequencies of the MVS was then performed in order to better understand the response of the final device. From this, two important results were found. Firstly, for every configuration of the MVS an underlying 350Hz was observed which corresponded to the dominant frequency of the vowel ‘u’. This frequency was attributed to the resonance of the entire length of the pipe and explains why the device always had an undertone of ‘u’. The second result was that the other English vowels could be produced by matching their fundamental frequencies with the frequencies in the mapping of the MVS. By doing this, the dominant frequencies of all eight vowels in Table 1 were able to be matched to within 10% and the minor frequencies to within 5-30%.  15  4. Project Deliverables 4.1 List of Deliverables From the Project Proposal, the deliverables of the project will include the Final Engineering Recommendation Report, the Mechanical Voice Synthesiser, recorded demonstrations of the device functioning, comparisons of spectrum plots obtained from real speech and the device as well as documentation describing the system components, including all of the accompanying design drawings. Most of these deliverables such as the comparisons between spectrum plots and the documentation describing the device components will be included in the Final Recommendation Report. The final device, however, will be delivered in person and the recordings of the specific vowels will be included as an attachment to the Final Report.  4.2 Financial Summary Table 2 – Break-up of Project Expenses #  Description  Quantity  Vendor(s)  Cost  Purchased by:  1  Duck call  1  $15  Harish/Tristan  2  Plastic Tube (20 cm, 4.4 cm id)  1  Canadian Tire Phys Store  -  Project Lab  3  Duck call adapter (Lexan: 5 cm thick, 2.5 cm id, 4.4 cm od)  1  Phys Store  -  Project Lab  Phys & Astro Department  4  Large Cavity Adjuster (Lexan: 2 cm thick, 5.2 cm id, 7 cm od)  1  Phys Store  -  Project Lab  Phys & Astro Department  5  Small Cavity Adjuster (Lexan: 0.84 cm thick, 5.2 cm id, 7 cm od)  1  Phys Store  -  Project Lab  Phys & Astro Department  6  Large Magnets  4  -  Project Lab  7  Small Magnets  30  -  Project Lab  9  Small Diaghram (Teflon: 0.84 cm thick, 1 cm id, 4.35 cm od)  1  Phys Store Phys Store Phys Store  -  Project Lab  Phys & Astro Department Phys & Astro Department Phys & Astro Department  16  To be funded by: Phys & Astro Department Phys & Astro Department  10  11  12  13  14  15  16  17  18  Proto 0 large pipes (Alum: 14 cm long, 3.2 cm id) Proto 0 small pipes (Alum: 5 cm long, 1.3 cm id) Proto 1 pipes (Alum: 223.9 mm long, 31.75 mm id) Proto 1 donuts (Lexan: 53.95 mm long, 12.70 mm id) Proto 2 pipes (Alum: 194.45 mm long, 31.75 mm id) Proto 2 small id donut (Lexan: 12.7 mm thick, 12.7 mm id) Proto 2 large id donut (Lexan: 31.75 mm thick, 15.875 mm id) Proto 3 pipes (Alum: 90.25 mm long, 31.75 mm id) Proto 3 donuts (Lexan: 6.35 mm /12.7 mm /12.7 mm long, 23.9 mm /15mm /22mm id)  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  1  Phys Store  -  Project Lab  Phys & Astro Department  4.3 Ongoing commitments by team members After consultation with the Project Sponsors, there are no ongoing commitments for team members after submittal of the Final Report.  17  5. Recommendations 1. While our theory was successful in predicting the resonant frequencies for the Single Helmholtz and our prototypes, it was unsuccessful at accurately predicting the behaviour of our final device. There are two possible causes for this discrepancy; either the theory is an oversimplification of the acoustical system or the final design, itself, is flawed. In the first case, it may be that the Lumped Parameter Analysis technique does not take into account the complexity of the system. That is, the assumptions and approximations used are not correct for our particular system. To solve this, it is recommended that the theory be revisited in a less generalized manner. In the second case, it may be that problems such as leakage and vibration of the diaphragms in our final device make the behaviour of the system unpredictable. To correct this, it is suggested that the design be revisited so that the sealing and stiffness of the diaphragms is improved. 2. While the goal of obtaining vowel sounds from a mechanical model of the human vocal tract was completed successfully, there was still some error in the location of the formant centers. That is, for some vowels, the spectrum did not align exactly with the expected IPA formant centers. To remedy this, the mapping of the final device could be done with higher precision so that the formant frequencies between those already measured are obtained. This could easily be done by decreasing the step size in our testing procedure to less than 1 cm. Furthermore, the precision could be increased by using a more accurate analysis program when finding the formant frequencies. 3. Another issue that might be fixed in the future is the presence of a low frequency tone in all of our recorded spectra. This tone, due to the final devices pipe resonance, is the dominant formant for the vowel ‘u’. Therefore, it causes all of our vowels to sound similar to a ‘u’. To solve this problem, the length of the total device should either be extended or shortened to move the pipe resonance to a frequency below or above the frequency range for vowel formants.  4. In the future, the device might be extended to include consonants by adding the feature of being able to stop the flow of air and by adding a resonant chamber for the nasal cavity. Further research will need to be done, to properly implement these additions.  5. To use the final device as a physics demo, it is recommended that the vowels ‘u’ and ‘i’ be used as examples as they correspond to particularly nice outputs in terms of frequency spectrum and sound. These vowels correspond to the following dimensions, tube 1 measured from the input end and tube 2 measured from the position of the adjuster of tube 1:  ‘u’: Tube 1 = 3 cm, Tube 2 = 2 cm ‘i’: Tube 1 = 14 cm, Tube 2 = 0 cm  18  Appendix A - Theory  19  20  21  22  Appendix B – Design Drawing  23  Appendix C – Final Data Results obtained from mapping the MVS Tube 1  Tube 2  F1  F2  F3  F4  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  466.2 422.2 487 457.4 427.8 427.8 413 398.2 427.8 442.6 427.8 413 457.4 442.6 442.6 413 398.2  1301 1052 975.6 901.5 871.9 945.9 945.9 1020 1035 1109 1198 1227 1434 1316 1257 1227 1138  2532 1653 1745 1879 1923 1997 2352 2412 1997 1923 1760 1686 1434 1316 1257 1227 1138  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  413 413 413 442.6 442.6 427.8 442.6 398.2 427.8 442.6 442.6 442.6 442.6 442.6 427.8  945.9 931.1 945.9 886.7 960.8 960.8 975.6 1286 1375 1286 1257 1183 1183 1124 1109  1642 1879 1938 2115 1568 960.8 975.6 1286 1375 1286 1257 1183 1183 1124 1109  2 2  1 2  442.6 442.6  916.3 901.5  1701 1538 24  4469 merged 4188 2338 2278 2086  phi  o  3122 merged 2767 2426 2160 2086 1997 1908 1745 1500 1300  2 2 2 2 2 2 2 2 2 2 2 2  3 4 5 6 7 8 9 10 11 12 13 14  442.6 383.4 413 442.6 413 442.6 427.8 427.8 413 427.8 442.6 413  857.1 916.3 1079 1124 1168 1168 1286 1257 1035 1005 1005 1005  1509 1420 1079 1124 1168 1168 1286 1257 1035 1005 1005 1005  3 3 3 3 3 3 3 3 3 3 3 3 3  1 2 3 4 5 6 7 8 9 10 11 12 13  380 380 380 380 380 360 340 380 380 380 380 380 380  780 820 880 850 1100 1100 1050 1000 900 900 900 850 850  1900 1500 1300 1230 1100 1100 1050 1000 900 900 900 850 850  3500 merged 2800 2600 2100 2000 1950 1800 1650 1500  4 4 4 4 4 4 4 4 4 4 4 4  1 2 3 4 5 6 7 8 9 10 11 12  380 400 380 400 380 360 380 360 350 320 320 320  850 880 880 950 1000 950 900 880 880 800 820 750  1900 1500 1400 1300 1000 950 900 880 880 800 820 750  3500 merged 3000 2600 2300 2100 1900 1800 1700  350  900  1800  5 1  25  3477 merged 3078 2648 2426 2175 2101 1923 1657 1583 1538  ah  u  y  5 5 5 5 5 5 5 5 5 5  2 3 4 5 6 7 8 9 10 11  350 350 340 340 340 340 340 340 340 320  930 900 900 900 900 850 850 830 820 750  1500 900 900 900 900 850 850 830 820 750  6 6 6 6 6 6 6 6 6 6  1 2 3 4 5 6 7 8 9 10  380 380 380 380 380 380 380 380 380 350  900 960 990 940 900 850 830 800 800 780  1800 1400 1400 1400 900 850 830 800 800 780  2800 merged 1600 1900 2200 2100 1900  7 7 7 7 7 7 7 7 7  1 2 3 4 5 6 7 8 9  320 320 320 310 310 310 310 310 310  1000 1000 1000 930 900 880 850 750 740  1800 1500 1000 930 900 880 850 750 740  4800 merged 4300 3500 2500 2400 2200 2000  8 8 8 8 8 8 8 8  1 2 3 4 5 6 7 8  340 340 340 340 320 320 320 320  1050 1100 1000 950 900 850 850 800  2450 2300 1800 1600 1350 850 850 800  2200 merged 2200 2100  26  3400 merged 3300 3200 3000 2700 2400 2000 1900 1800  ae  a  e  9 9 9 9 9 9 9  1 2 3 4 5 6 7  300 300 300 300 300 300 300  1100 1050 1000 950 900 900 800  2200 2100 2000 2100 2050 1950 1950  10 10 10 10 10 10  1 2 3 4 5 6  320 310 310 310 300 300  1150 1100 1000 950 900 850  2200 2000 1900 1850 1800 1800  11 11 11 11 11  1 2 3 4 5  340 340 320 320 300  1260 1100 1000 950 880  1700 1770 1750 1700 1700  12 12 12 12  1 2 3 4  340 340 330 330  1230 1140 1000 900  1960 1740 1640 1580  13 1 13 2 13 3  340 340 310  1200 1000 960  1700 1550 1460  14 0 14 1 14 2  340 340 340  1300 1200 1000  2400 2100 1600  15 0 15 1  340 340  1150 1100  2300 3500  16 0  340  1150  2100  27  i  Plot of mapped data  28  Plot of data from theory  29  References Beranek, Leo Leroy. Acoustics. New York, NY: Published by the American Institute of Physics for the Acoustical Society of America, 1986. Print. "Formant - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 16 Feb. 2011. <http://en.wikipedia.org/wiki/Formant>.  Olson, Harry Ferdinand. Acoustical Engineering. Princeton, NJ: Van Nostrand, 1957. Print. Olson, Harry Ferdinand. Elements of Acoustical Engineering. New York: Van Nostrand, 1943. Print. "Tutorial 02." Scribd. N.p., n.d. Web. 7 Feb. 2011. <http://www.scribd.com/doc/36953275/Tutorial-02>.  30  

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