Modeling and quantization techniques for speech compression systems

OF THE DISSERTATION Modeling and Quantization Techniques for Speech Compression Systems by William R. Gardner Doctor of Philosophy in Electrical Engineering (Communication Theory and Systems) University of California, San Diego, 1994 Professor Bhaskar D. Rao, Chair This dissertation introduces new modeling and quantization techniques for improving the performance of speech compression systems. In Part I, mixed-phase all-pole models are proposed for modeling the spectral magnitude and phase information in voiced speech. Mathematical and physiological motivations for the models are given. Time domain and frequency domain parameter estimation algorithms are described, including e cient least-squares based algorithms and algorithms which incorporate perceptual masking e ects. It is shown that high quality voiced speech can be reconstructed from a fourteenth order mixed-phase allpole model. In Part II, vector quantization of the lter coe cients of all-pole models is investigated. A theoretical analysis of high rate vector quantizers trained using xiii suboptimal distortion measures is presented. It is shown that, at high rate, the quantization distortion approaches a quadratically weighted error measure. The quadratic weighting matrix is a \sensitivity matrix," which is a generalization of the scalar sensitivity concept. The diagonal elements of the sensitivity matrix relate to the sensitivities of the individual scalar parameters, and the o -diagonal elements relate to the interactions which occur when multiple parameters are quantized simultaneously. The sensitivity matrices, with respect to the Log Spectral Distortion measure, for standard linear predictive coding (LPC) lter coe cients, re ection coe cients, log area ratios, arcsine coe cients, and line spectral pair (LSP) frequencies are described. In particular, it is shown that the sensitivity matrix for the LSP frequencies is diagonal, implying that a vector quantizer trained by minimizing a weighted mean squared error measure in the LSP frequencies can provide optimal performance at high rate. Computationally e cient algorithms for computing the sensitivity matrices are described. Finally, the theoretical results are compared with experimental data and are shown to be valid for quantization rates of interest. xiv Introduction to Speech Compression The transmission and storage of speech are widespread in modern telecommunication systems. Reducing the amount of information required to faithfully reproduce a speech signal can signi cantly increase the capacity of digital speech tranmission and storage systems. For example, most modern digital cellular and satellite systems use speech compression algorithms to increase the capacity of the systems above that which can be achieved by analog systems, which typically do not use speech compression algorithms. Voice-mail systems often use speech compression algorithms to increase the amount of storage time given a nite memory or disk size. The eld of speech compression is dedicated to nding new, more e cient ways of reducing the transmission or storage rates for speech while maintaining high quality in the reconstructed speech. Compression can be achieved in several ways. First, the speech signal contains signi cant redundant information. This information can be removed before transmission or storage, reducing the data rate needed. Much of the redundancy can be identi ed by studying and modeling the production of speech by the human vocal apparatus. Improved models for the production of speech have resulted in more e cient removal of the redundancy in the speech signal. Second, the ear is an imperfect listening device and some types of distortion added by a speech compression system are inaudible. The resulting compressed speech signal, 1 2 although not \bit-for-bit exact" with the original speech signal, may be perceptually equivalent to the original signal, or the perceptual degradation may be minimal. The study and modeling of the perception of speech has led to methods for removing only the perceptually insigni cant information from the speech signal, resulting in greater compression. Most speech compression algorithms can be divided into two parts: modeling and quantization. Typically, a compression algorithm rst extracts model parameters which \best t" a given time segment of speech, and then quantizes these model parameters in a way which minimizes the perceptual distortion. The quality of the reconstructed speech can be improved by techniques which more e ciently model the perceptually important information in the speech signal, and by techniques which more e ciently quantize the model parameters. This work describes improved modeling and quantization techniques. This dissertation is divided into two parts. In Part I, the problem of parsimoniously modeling the voiced speech signal is described, and mixed-phase all-pole lter models which parameterize both spectral magnitude and spectral phase information of the voiced speech signal are introduced. Mathematical and physiological motivations for the mixed-phase models are given. Algorithms are proposed for determining the model parameters which accurately model a given time segment of a voiced speech signal. Both production models and perception models for speech are incorporated to improve the quality of the speech reconstructed from the extracted model parameters. It is shown that high quality voiced speech can be reconstructed using a frequency domain based model, where the spectral magnitude and phase information is extracted from a fourteenth order mixed-phase all-pole model. 3 In Part II, the quantization of the all-pole lter coe cients is investigated, and the results of Part II can be applied to both traditional minimum-phase linear predictive coding (LPC) lters as well as mixed-phase lter models such as those described in Part I. The distortion measure most often cited as being an accurate perceptual measure for LPC quantization is the Log Spectral Distortion (LSD) measure. However, due to the complexity of the LSD measure, it is typically not used in real-time implementations, and often other less complex measures are used. Part II presents theoretical results for approximating the performance of high rate quantizers using these less complex measures. It is shown that at high rate, the LSD measure converges to a quadratically weighted error measure. The quadratic weighting matrix is termed the \sensitivity matrix," which is a generalization of the scalar sensitivity concept. The diagonal elements of the sensitivity matrix relate to the sensitivities of the individual scalar parameters, and the o -diagonal elements relate to the interactions which occur when multiple parameters are quantized simultaneously. Mean squared error (MSE) and weighted mean squared error (WMSE) measures are investigated for the popular representations of LPC lter coe cients, including re ection coe cients (or PARCOR coe cients), log area ratios, arcsine coe cients, and line spectral pair (LSP) frequencies, and these measures are compared with the optimal, sensitivity weighted measures. In particular, it is shown that the sensitivitymatrix for the LSP frequencies is diagonal, implying that a WMSE measure of the LSP frequencies approaches the LSD measure at high rates. Computationally e cient algorithms for computing the sensitivity matrices of all of the above mentioned representations are given. Finally, the theoretical results are compared with experimental results, and are shown to be valid for quantization rates of interest. Part I Mixed-Phase All-Pole Models for Voiced Speech 4 Chapter