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UBC Theses and Dissertations

Optimal pre and postfiltering of noisy sampled signals - particular applications to PAM, PCM and DPCM communication systems. Chan, Donald


In many control, data-processing, and communication systems, sampling is an inherent part of the system. If the time-continuous input signal is nonbandlimited, and noise is introduced in the system, an unavoidable error exists between the actual reconstructed signal and the desired time-continuous output signal. This error can be reduced by the suitable choice of prefilter prior to sampling and by the suitable choice of post-filter for reconstructing the time-continuous signal from the samples. In this thesis, an algorithm for determining the jointly optimal pre and post-filters which minimize the frequency weighted mean-integral-squared error of the system is presented, and the validity of the algorithm is proved. In the analysis, no restrictions are placed on the input signal spectrum or the noise spectrum, and the cross-correlation between signal and noise is taken into account. Applications of the optimization algorithm to M-channel time-multiplexed PAM systems, PCM systems with digital channels errors, and DPCM systems are considered. Performance characteristics, showing mean-squared error and inband signal-to-noise ratio versus channel signal-to-noise ratio, are determined explicitly for optimal pre and postfiltered PAM and PCM systems with first-order Butterworth input spectrum. These characteristics are compared with those of PAM and PCM systems which use suboptimal filtering schemes and with the optimal performance theoretically attainable. Performance characteristics, showing mean-squared error versus channel capacity, are also determined for PAM, PCM, and DPCM systems when the systems parameters are optimized to yield the least mean-squared error for a given channel capacity. Because of the subjective nature of speech, the effect of pre and postfilters in PAM, PCM and DPCM communication systems for speech transmission is studied by simulation methods and evaluated with subjective tests. Weak noise pre and postfilters (WNF), which yield virtually the same performance as optimal pre and postfilters, are considered in the subjective evaluation, in addition to lowpass pre and postfilters (LPF). The digital simulation facilities and the subjective testing methods are described, and the subjective results interpreted. It was observed that no significant subjective improvement resulted when WNF were used in place of LPF in PAM and DPCM systems. In PCM systems, significant differences in WNF and LPF subjective performances could exist. Using the analytical results, an explanation for the subjective behaviour is presented.

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