0.14 Lab 9b - speech processing (part 2)

Questions or comments concerning this laboratory should be directedto Prof. Charles A. Bouman, School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907;(765) 494-0340; bouman@ecn.purdue.edu

Introduction

This is the second part of a two week experiment. During the first weekwe discussed basic properties of speech signals, and performed some simple analyses in the time and frequencydomain.

This week, we will introduce a system model for speech production. We will cover some background on linear predictive coding , and the final exercise will bring all the prior material together in aspeech coding exercise.

A speech model

From a signal processing standpoint, it is very useful to think of speech production in terms of a model, as in [link] . The model shown is the simplest of its kind,but it includes all the principal components. The excitations for voiced and unvoiced speech are represented by animpulse train and white noise generator, respectively. The pitch of voiced speech is controlled by the spacing betweenimpulses, $T_p$ , and the amplitude (volume) of the excitation is controlled by the gain factor $G$ .

As the acoustical excitation travels from its source (vocal cords, or a constriction), the shape of the vocal tract alters the spectralcontent of the signal. The most prominent effect is the formation of resonances, whichintensifies the signal energy at certain frequencies (called formants ). As we learned in the Digital Filter Design lab, the amplification of certainfrequencies may be achieved with a linear filter by an appropriate placement of poles in the transfer function.This is why the filter in our speech model utilizes an all-pole LTI filter. A more accurate model might include a few zeros in the transfer function,but if the order of the filter is chosen appropriately, the all-pole model is sufficient.The primary reason for using the all-pole model is the distinct computational advantage in calculating the filter coefficients, as will be discussedshortly.

Recall that the transfer function of an all-pole filter has the form

where $P$ is the order of the filter. This is an IIR filter that maybe implemented with a recursive difference equation. With the input $G·x\left(n\right)$ , the speech signal $s\left(n\right)$ may be written as

Keep in mind that the filter coefficients will change continuously as the shape of the vocal tract changes, but speech segments of anappropriately small length may be approximated by a time-invariant model.

This speech model is used in a variety of speech processing applications, including methods of speech recognition, speech coding for transmission,and speech synthesis. Each of these applications of the model involves dividing the speech signalinto short segments, over which the filter coefficients are almost constant. For example, in speech transmission the bit rate can be significantlyreduced by dividing the signal up into segments, computing and sending the model parameters for each segment (filter coefficients, gain, etc.),and re-synthesizing the signal at the receiving end, using a model similar to [link] . Most telephone systems use some form of this approach.Another example is speech recognition. Most recognition methods involve comparisons between shortsegments of the speech signals, and the filter coefficients of this model are often used in computing the “difference" between segments.