University of California at Los Angeles
Department of Electrical Engineering
EE 214A: Digital Speech Processing, Winter 2002

Wideband Speech Coding
with Linear Predictive Coding
(LPC)

Professor:
Abeer Alwan

Authors:
Ozgu Ozun
Philipp Steurer
Daniel Thell

Abstract

Wideband speech signals of 2 males and 2 females were coded using an improved version of Linear Predictive Coding (LPC). The sampling frequency was at 16 kHz and the bit rate was at 15450 bits per second, where the original bit rate was at 128000 bits per second. The tradeoffs between the bit rate, end-to-end delay, speech quality and complexity were analyzed. Simulations as well as Segmental SNR evaluations were done to analyze the performance of the implemented algorithm.

Table of Contents

ABSTRACT

1 INTRODUCTION

2 BACKGROUND

3 PROJECT DESCRIPTION

3.1 METHODOLOGY
3.2 PRE-EMPHASIS FILTER
3.3 QUANTIZATION OF LPC-COEFFICIENTS

4 VOICE-EXCITED LPC VOCODER

4.1 DCT OF RESIDUAL SIGNAL
4.2 PERFORMANCE ANALYSIS

4.2.1 Bit Rates
4.2.2 Overall Delay of the System
4.2.3 Computational Complexity
4.2.4 Objective Performance Evaluation

5 DISCUSSION OF RESULTS

5.1 QUALITY

5.1.1 Subjective quality
5.1.2 Segmental signal to noise ratio

5.2 QUALITY-PERFORMANCE TRADEOFFS

5.2.1 Bit rate performance
5.2.2 Delay and computational complexity

6 CONCLUSIONS

7 REFERENCES

8 APPENDIX

8.1 MAIN FILE
8.2 LPC OUTPUT INFORMATION GENERATION
8.3 PLAIN LPC VOCODER

8.3.1 Main file
8.3.2 Plain LPC decoder

8.4 VOICE-EXCITED LPC VOCODER

8.4.1 Main File
8.4.2 Voice-excited LPC decoder

WAVE FILES

1 Introduction

Speech coding has been and still is a major issue in the area of digital speech processing. Speech coding is the act of transforming the speech signal at hand, to a more compact form, which can then be transmitted with a considerably smaller memory. The motivation behind this is the fact that access to unlimited amount of bandwidth is not possible. Therefore, there is a need to code and compress speech signals. Speech compression is required in long-distance communication, high-quality speech storage, and message encryption. For example, in digital cellular technology many users need to share the same frequency bandwidth. Utilizing speech compression makes it possible for more users to share the available system. Another example where speech compression is needed is in digital voice storage. For a fixed amount of available memory, compression makes it possible to store longer messages [1].

Speech coding is a lossy type of coding, which means that the output signal does not exactly sound like the input. The input and the output signal could be distinguished to be different. Coding of audio however, is a different kind of problem than speech coding. Audio coding tries to code the audio in a perceptually lossless way. This means that even though the input and output signals are not mathematically equivalent, the sound at the output is the same as the input. This type of coding is used in applications for audio storage, broadcasting, and Internet streaming [2].

Several techniques of speech coding such as Linear Predictive Coding (LPC), Waveform Coding and Subband Coding exist. The problem at hand is to use LPC to code 2 male and 2 female speech sentences. The speech signals that need to be coded are wideband signals with frequencies ranging from 0 to 8 kHz. The sampling frequency should be at 16 kHz with a maximum end-to-end delay of 100 ms. Different types of applications have different time delay constraints. For example in network telephony only a delay of 1ms is acceptable, whereas a delay of 500 ms is permissible in video telephony [3]. Another constraint at hand is not to exceed an overall bit rate of 16 kbps. When all is said and done, the system must have less than 20 million operations per second (MOPS).

The speech coder that will be developed is going to be analyzed using both subjective and objective analysis. Subjective analysis will consist of listening to the encoded speech signal and making judgments on its quality. The quality of the played back speech will be solely based on the opinion of the listener. The speech can possibly be rated by the listener either impossible to understand, intelligible or natural sounding. Even though this is a valid measure of quality, an objective analysis will be introduced to technically assess the speech quality and to minimize human bias. The objective analysis will be performed by computing Segmental Signal to Noise Ratio (SEGSNR) between the original and the coded speech signal. Furthermore, an analysis on the study of effects of bit rate, complexity and end-to-end delay on the speech quality at the output will be made. The report will be concluded with the summary of results and some ideas for future work.

2 Background

There are several different methods to successfully accomplish speech coding. Some main categories of speech coders are LPC Vocoders, Waveform and Subband coders. The speech coding in this project will be accomplished by using a modified version of LPC-10 technique. Linear Predictive Coding is one possible technique of analyzing and synthesizing human speech. The exact details of the analysis and synthesis of this technique that was used to solve our problem will be discussed in the methodology section. Only an overview will be included in this section, along with the previously mentioned other types of coding techniques.

LPC method has been used for a long time. Texas Instruments had developed a monolithic PMOS speech synthesizer integrated circuit as early as 1978. This marked the first time the human vocal tract had been electronically duplicated on a single chip of silicon [5]. This one of the first speech synthesizer used LPC to accomplish successful synthesis. LPC makes coding at low bit rates possible. For LPC-10, the bit rate is about 2.4 kbps. Even though this method results in an artificial sounding speech, it is intelligible. This method has found extensive use in military applications, where a high quality speech is not as important as a low bit rate to allow for heavy encryption of secret data. However, since a high quality sounding speech is required in the commercial market, engineers are faced with using other techniques that normally use higher bit rates and result in higher quality output. In LPC-10 vocal tract is represented as a time-varying filter and speech is windowed about every 20 ms. For each frame, the gain and only 10 of the coefficients of a linear prediction filter are coded for analysis and decoded for synthesis. In 1996, LPC-10 was replaced by mixed-excitation linear prediction (MELP) coder to be the United States Federal Standard for coding at 2.4 kbps. This MELP coder is an improvement to the LPC method, with some additional features that have mixed excitation, aperiodic pulses, adaptive spectral enhancement and pulse dispersion filtering as mentioned in [4].

Waveform coders on the other hand, are concerned with the production of a reconstructed signal whose waveform is as close as possible to the original signal, without any information about how the signal to be coded was generated. Therefore, in theory, this type of coders should be input signal independent and work for both speech and non-speech input signals [4]. Waveform coders produce a good quality of speech signals above bit rates of 16 kbps. However, if the bit rate is decreased below 16 kpbs, the quality deteriorates quickly. One form of waveform coding is Pulse Code Modulation (PCM). This type of waveform coding involves sampling and quantizing the input signal. PCM is a memoryless coding algorithm as mentioned in [4]. Another type of PCM is Differential Pulse Code Modulation (DPCM). This method quantizes the difference between the original and the predicted signals. This method involves prediction of the next sample from the previous samples. This is possible since there is a correlation in speech samples because of the effects of the vocal tract and the vibrations in the vocal cords [6]. It is possible to improve the predictor as well as the quantizer in DPCM if they are made adaptive, in order to match the characteristics of the speech that is to be coded. This type of coders is called Adaptive Differential Pulse Code Modulation (ADPCM).

One other type of speech coders is called the Subband coders. This type of coding involves filter bank analysis to be undertaken in order to filter the input signal into several frequency bands. Bit allocation is done to each band by a certain criterion [4]. Presently however, Subband coders are not widely used for speech coding. It is very difficult to create high quality speech by using low bit rates with this technique. As suggested in [4], Subband coding is mostly utilized in the medium to high bit rate applications of speech coding.

3 Project Description

3.1 Methodology

Fig. 3-1: Block diagram of an LPC vocoder.

In this section an explanation of the LPC speech coding technique will be given. The specific modifications and additions done to improve this algorithm will also be covered. However, before jumping into the detailed methodology of our solution, it will be helpful to give a brief overview of speech production. Speech is produced when velum is lowered to make it acoustically coupled with the vocal tract. Nasal sounds of speech are produced this way [7]. Speech signals consist of several sequences of sounds. Each sound can be thought of as a unique information. There are voiced and unvoiced types of speech sounds. The fundamental difference between these two types of speech sounds comes from the way they are produced. The vibrations of the vocal cords produce voiced sounds. The rate at which the vocal cords vibrate dictates the pitch of the sound. On the other hand, unvoiced sounds do not rely on the vibration of the vocal cords. The unvoiced sounds are created by the constriction of the vocal tract. The vocal cords remain open and the constrictions of the vocal tract force air out to produce the unvoiced sounds [7].

LPC technique will be utilized in order to analyze and synthesize speech signals. This method is used to successfully estimate basic speech parameters like pitch, formants and spectra. A block diagram of an LPC vocoder can be seen in Fig.3-1. The principle behind the use of LPC is to minimize the sum of the squared differences between the original speech signal and the estimated speech signal over a finite duration. This could be used to give a unique set of predictor coefficients [7]. These predictor coefficients are normally estimated every frame, which is normally 20 ms long. The predictor coefficients are represented by ak. Another important parameter is the gain (G). The transfer function of the time-varying digital filter is given by:

The summation is computed starting at k=1 up to p, which will be 10 for the LPC-10 algorithm, and 18 for the improved algorithm that is utilized. This means that only the first 18 coefficients are transmitted to the LPC synthesizer. The two most commonly used methods to compute the coefficients are, but not limited to, the covariance method and the auto-correlation formulation. For our implementation, we will be using the auto-correlation formulation. The reason is that this method is superior to the covariance method in the sense that the roots of the polynomial in the denominator of the above equation is always guaranteed to be inside the unit circle, hence guaranteeing the stability of the system H (z) [7]. Levinson - Durbin recursion will be utilized to compute the required parameters for the auto-correlation method. The block diagram of simplified model for speech production can be seen in Fig. 3-2 as provided in [1].

Fig. 3-2 Simplified model for speech production

The LPC analysis of each frame also involves the decision-making process of concluding if a sound is voiced or unvoiced. If a sound is decided to be voiced, an impulse train is used to represent it, with nonzero taps occurring every pitch period. A pitch-detecting algorithm is employed to determine to correct pitch period / frequency. We used the autocorrelation function to estimate the pitch period as proposed in [7]. However, if the frame is unvoiced, then white noise is used to represent it and a pitch period of T=0 is transmitted. Therefore, either white noise or impulse train becomes the excitation of the LPC synthesis filter. It is important to re-emphasize that the pitch, gain and coefficient parameters will be varying with time from one frame to another.

3.2 Pre-emphasis Filter

From the speech production model it is known that the speech undergoes a spectral tilt of -6dB/oct. To counteract this fact a pre-emphasis filter of the following form is used:

The frequency response of a typical pre-emphasis filter is shown in Fig. 3-3 as well as its inverse filter. This is involved during the synthesis / reconstruction of the speech signal and is as follows:

Fig. 3-3: Frequency response of the pre-emphasis filter and its inverse filter

The main goal of the pre-emphasis filter is to boost the higher frequencies in order to flatten the spectrum. To give an idea of the improvement made by this filter the reader is referred to the plotted frequency spectrum in Fig. 3-4 of the vowel /i/ in the word nine. It can be seen how the spectrum is flattened. This improvement leads to a better result for the calculation of the coefficients using LPC. There are higher peaks visible for higher frequencies in the LPC-spectrum as can be seen in Fig. 3-5. Clearly, the coefficients corresponding to higher frequencies can be better estimated.

Fig. 3-4: Frequency spectrum of the vowel /i/ in the word nine.

Fig. 3-5: Spectrum of the LPC model for the vowel /i/ in the word nine.

3.3 Quantization of LPC-coefficients

Usually direct Quantization of the predictor coefficients is not considered. To ensure stability of the coefficients (the poles and zeros must lie within the unit circle in the z-plane) a relatively high accuracy (8-10 bits per coefficients) is required. This comes from the effect that small changes in the predictor coefficients lead to relatively large changes in the pole positions. There are two possible alternatives discussed in [7] to avoid the above problem. Only one of them is explained here, namely the partial reflection coefficients (PARCOR). These are intermediate values during the calculation of the well-known Levinson-Durbin recursion. Quantizing the intermediate values is less problematic than quantifying the predictor coefficients directly. Thus, a necessary and sufficient condition for the PARCOR values is . Should the poles not lie inside the unit circle one just flips the location, as we discussed in class.

4 Voice-excited LPC Vocoder

As the test of the sound quality of a plain LPC-10 vocoder showed, the weakest part in this methodology is the voice excitation. It is know from the literature [7] that one solution to improve the quality of the sound is the use of voice-excited LPC vocoders. Systems of this type have been studied by Atal et al. [8] and Weinstein [9]. Fig. 4-1 shows a block diagram of a voice-excited LPC vocoder. The main difference to a plain LPC-10 vocoder, as showed in Fig. 3-1, is the excitation detector, which will be explained in the sequel.

Fig. 4-1: Block diagram of a voice-excited LPC vocoder.

The main idea behind the voice-excitation is to avoid the imprecise detection of the pitch and the use of an impulse train while synthesizing the speech. One should rather try to come up with a better estimate of the excitation signal. Thus the input speech signal in each frame is filtered with the estimated transfer function of LPC analyzer. This filtered signal is called the residual. If this signal is transmitted to the receiver one can achieve a very good quality. The tradeoff, however, is paid by a higher bit rate, although there is no longer a need to transfer the pitch frequency and the voiced / unvoiced information. We therefore looked for a solution to reduce the bit rate to 16 kbits/sec, which is described in the following section.

4.1 DCT of residual signal

First of all, for a good reconstruction of the excitation only the low frequencies of the residual signal are needed. To achieve a high compression rate we employed the discrete cosine transform (DCT) of the residual signal. It is known, that the DCT concentrates most of the energy of the signal in the first few coefficients. Thus one way to compress the signal is to transfer only the coefficients, which contain most of the energy. Our tests and simulations showed that these coefficients could even be quantized using only 4 bits. The receiver simply performs an inverse DCT and uses the resulting signal to excite the voice.

4.2 Performance Analysis

4.2.1 Bit Rates

In the sequel the necessary bit rates of the two solutions are computed. The bit rate for a plain LPC vocoder is shown in Table 4-1 and the bit rate for a voice-excited LPC vocoder with DCT is printed in Table 4-2. The following parameters were fixed for the calculation:

· Speech signal bandwidth B = 8 kHz
· Sampling rate Fs = 16000 Hz (or samples/sec.)
· Window length (frame): 20 ms
which results in 320 samples per frame by the given sampling rate Fs
· Overlapping: 10 ms (overlapping is needed for perfect reconstruction)
hence: the actual window length is 30ms or consists of 480 samples
· There are 50 frames per second
· Number of predictor coefficients of the LPC model = 18 (see calculation in ….)

Table 4-2: Bit rate for voice-excited LPC vocoder with DCT

4.2.2 Overall Delay of the System

The overall delay of the systems tells one how long it takes from the input of the first sample of speech into the system until the first sample of the synthesized speech is available at the output of the system. This is clearly an important number, since one would like to process the data in real-time. If, for example, an LPC vocoder is used in a communication system, e.g. a cellular phone, one does not accept a large delay of the transmitted speech signal. Humans are able to perceive delays of speech within a several hundred of milliseconds during a talk at the telephone. For our project the limit was set to a maximum allowed value of 100 ms.

For both of our proposed solutions the overall delay is 30 ms, since the window length is 20ms and the overlapping is 10ms. In other words, the systems needs to have at least 30 ms of input data before the first calculation can be done. Of course, the calculation time needs to be added to this delay. It is not possible to come up with this number, since we employed Matlab for our simulations. The calculation time therefore depends on the speed of the used computer. We therefore just provide the reader a way to calculate this number on its own for a particular microprocessor system, for which the processor speed is known. This simply requires the knowledge of the computational complexity of the system, which is provided in section 4.2.3 of this report.

4.2.3 Computational Complexity

Again, the same parameters, as stated in section 4.2.1, are fixed for the calculations. All numbers show the multiplications or additions required per frame. This number needs to be multiplied by the number of frames of a given speech signal.

· Calculation of the LPC coefficients. The Levinson-Durbin recursion requires O(p2) floating point operations per second (FLOPS). In our case p = 18, hence this step requires 324 FLOPS per frame.
· The pre-emphasis filter needs 480 additions and 480 multiplications, which is equal to 960 operations.
· The cross-correlation consists of 480 additions and 480 multiplications, which is equal to 960 operations.
· The reconstruction of the LPC needs about 480*18 additions and 480*18 multiplications, which is equal to 17280 operations.
· The inverse filter requires again 480 additions and 480 multiplications, which is equal to 960 operations

Hence, the total number of operations for the plain LPC vocoder is 20484 operations per frame. The sentences in section 4.2.4 typically contain of about 150 frames at 50 frames/second. Thus, the computational complexity for the plain LPC vocoder is about 1 MFLOPS (Mega-Flops).

For the voice-excited vocoder the calculation of the cross-correlation is not needed but the discrete cosine transform and its inverse is needed instead. However, in the Matlab-code used, the cross-correlation is still computed as it was the case for the plain LPC vocoder. Therefore, the complexity is slightly increased.

· The DCT (if the fast algorithm is applied) requires 480 multiplications equaling 480 operations
· The inverse-DCT requires the same number of operations, namely 480 operations

The total number of FLOPS for the voice-excited LPC vocoder is therefore 21444 operations per frame. If we consider the same parameters as before, the computational complexity is roughly 1.07 MFLOPS. The improved sound quality makes up for the higher number of FLOPS.

4.2.4 Objective Performance Evaluation

We measured the segmental signal to noise ratio (SEGSNR) of the original speech file compared to the coded and reconstructed speech file using the provided Matlab-function "segsnr". The obtained results are as follows:

1) A Male speaker saying: "Kick the ball straight and follow through."
2) A Female speaker saying: "It's easy to tell the depth of a well."
3) A Male speaker saying: "A pot of tea helps to pass the evening."
4) A Female speaker saying: "Glue the sheet to the dark blue background."

Vocoder type	SNR 1	SNR 2	SNR 3	SNR 4
Plain LPC	-24.92 dB	-24.85 dB	-24.87 dB	-23.94 dB
Voice-excited LPC	0.5426 dB	0.7553 dB	0.5934 dB	0.2319 dB

Note that the calculation of the SNR requires the signals to be normalized before the ratio can be calculated.

5 Discussion of Results

5.1 Quality

5.1.1 Subjective quality

A comparison of the original speech sentences against the LPC reconstructed speech and the voice-excited LPC methods were studied. In both cases, the reconstructed speech has a lower quality than the input speech sentences. Both of the reconstructed signals sound mechanized and noisy with the output of plain LPC vocoder being nearly unintelligible. The LPC reconstructed speech sounds guttural with a lower pitch than the original sound. The sound seems to be whispered. The noisy feeling is very strong. The voice-excited LPC reconstructed file sounds more spoken and less whispered. The guttural feeling is also less and the words are much easier to understand. Overall the speech that was reconstructed using voice-excited LPC sounded better, but still sounded muffled.

The waveforms in Fig 5-1 give the same idea. The voice-excited waveform looks closer to the original sound than the plain LPC reconstructed one.

5.1.2 Segmental signal to noise ratio

Looking at the segmental SNR, computed in section 4.2.4, it is obvious that the first sound is very noisy, having a negative SNR. The noise in this file is even stronger than the actual signal. The voice-excited LPC encoded sound sounds far better, and its SNR, although barely, is in the positive side. However, even the speech coded with the improved voice-excited LPC does not sound exactly like the original signal.

It is noticeable that both the plain LPC and the voice-excited vocoders are not sensitive to the input sentence, the result is the same for a sentence with many voiced sounds and for a sentence with many fricatives or other unvoiced sounds. The good point is that any spoken sentence can be transmitted with the same overall results. The disadvantage is that we cannot focus on a specific aspect of the vocoder that would give much poorer results. To improve the quality, the overall system has to be improved. We cannot just improve the unvoiced sounds production to make the vocoder sound perfect.

5.2 Quality-performance tradeoffs

The LPC method to transmit speech sounds has some very good aspects, as well as some drawbacks. The huge advantage of vocoders is a very low bit rate compared to what is achieved for sound transmission. On the other hand, the speech quality achieved is quite poor.

Fig. 5-1: Waveform of the sentence "A pot of tea helps to pass the evening": a) original speech signal, b) LPC reconstructed speech signal, c) voice-excited LPC reconstructed speech signal

5.2.1 Bit rate performance

The achieved bit rate in both method are quite low, both under the required 16kbps. However, the voice-excited LPC coding requires a bandwidth twice as large as the plain LPC coding. This huge increase ends up with a better sound, but still not perfect. The computational complexity is nonetheless roughly the same.

Fig. 5-2: Speech quality vs. Bit rate trade-offs for different speech coding techniques

In the plain LPC vocoder, one tries to estimate the pitch and then excite the synthesizer with the estimated parameters. This results in a poor, almost unintelligible sentence. The lack of accuracy in determining the pitch and the exact mathematical excitation results in a huge degradation in the quality. Shifting to the voice excited LPC technique, the pitch and the binary choice in the method of excitation is dropped (7 bits per frame) but all the errors have to be sent.

The increase in the bit rate results then from a change in the excitation method. While impulse train was used as a source to the transfer function, the actual error made when computing the ak's, is now encoded and sent. Theoretically, a close to perfect reconstruction could be achieved if these errors were sent as floating points numbers. However, this would require a very large bandwidth. If we use 8 bits per error over the all frame, this would give 3840 bits per frame and then contribute to the overall bit rate with 192kbps. The errors are therefore compressed using an algorithm similar to the one used in the jpeg or mpeg compression. Taking the discrete cosine transform (DCT) and keeping only the 40 first coefficients (each quantized over 4 bits) allows a pretty good reconstruction of all the 480 errors in the frame. The maximum energies are located in the first few coefficients, so that the last 440 are assumed to be null.

However, we could notice that increasing the bit-rate of a vocoder is not the best idea since the improvement in the quality is not linear as can be seen in Fig. 5-2: Speech quality vs. Bit rate trade-offs for different speech coding techniques, as provided in [6]. If an increase in the required bandwidth significantly improves the quality at the beginning, the increase required after for the same amount of improvement is tremendously more important.

5.2.2 Delay and computational complexity

The overall delay of the system is hard to measure and depends on the machine used. However it can be estimated looking at the time between the launch of the program and the creation of the output file.

Both methods employed are of the same computational complexity. The voice-excited LPC method uses the original sound samples to produce the output sound while the plain LPC technique creates the output sound from more basic characteristics. The stronger link to the original signal in the voice-excited LPC method allows a more accurate reproduction of the sounds without increasing the complexity and the delay, since both concepts are closely linked.

As mentioned before, an idea to improve the overall quality could be, beside an increase in the required bandwidth, an increase in the vocoder complexity to transmit more information of more pertinent information with the same bandwidth. The overall delay of the system will therefore increase but our vocoder complexity is low enough to allow a complexity increase and still meet the project requirements regarding the FLOPS.

6 Conclusions

The results achieved from the voice excited LPC are intelligible. On the other hand, the plain LPC results are much poorer and barely intelligible. This first implementation gives an idea on how a vocoder works, but the result is far below what can be achieved using other techniques. Nonetheless the voice-excited LPC used gives understandable results and is not optimized. The tradeoffs between quality on one side and bandwidth and complexity on the other side clearly appear here. If we want a better quality, the complexity of the system should be increased or a larger bandwidth has to be used.

Since the voice-excited LPC gives pretty good results with all the required limitations of this project, we could try to improve it. A major improvement could come from the compression of the errors. If we can send them in a loss-less manner to the synthesizer, the reconstruction would be perfect. An idea could be the use of Huffman codes for the DCT coefficients. Many simulations have to be done to get the right code book.

This would reduce the bit rate, so that we can use the additional amount of bandwidth to improve quality. At least two possibilities could be considered. The first one would be an increase in bits used to quantize the DCT coefficients. The first coefficients would be more accurate resulting in closer reconstructed errors after the inverse DCT. The second way could be to increase the number of quantized coefficients. The result would be of the same kind, a more accurate reconstructed error array. The point is to know until what point an improve in one way is better than the other, since both should be improved to get a perfect file. Other kinds of coding techniques could be considered, all these methods will result in a complexity increase but the vocoder is simple enough to cope with it.

If someone wants to look for another way of improving the vocoder, he could look at the plain LPC vocoder and try to implement a covariance model. However, since there exists no fast algorithm for inverting the covariance matrix, the computational complexity can increase tremendously as well as the delay.

Finally, the excitation parameters, the weakest part in this implementation, could be looked at. All the unvoiced sounds cannot result from the same white Gaussian noise input. An analysis of this and the creation of a code book for unvoiced sounds could give better results. Again, statistical data and numerous simulations are needed.

7 References

[1] http://www.data-compression.com/speech.html

[2] http://www.bell-labs.com

[3] http://cslu.cse.ogi.edu/HLTsurvey/ch10node4.html

[4] M. H. Johnson and A. Alwan, "Speech Coding: Fundamentals and Applications", to appear as a chapter in the Encyclopedia of Telecommunications, Wiley, December 2002.

[5] http://www.ti.com/corp/docs/company/history/pmos.shtml

[6] http://www-mobile.ecs.soton.ac.uk

[7] L. R. Rabiner and R. W. Schafer, "Digital Processing of Speech Signals", Prentice- Hall, Englewood Cliffs, NJ, 1978.

[8] B. S. Atal, M. R. Schroeder, and V. Stover, "Voice-Excited Predictive Coding Systetm for Low Bit-Rate Transmission of Speech", Proc. ICC, pp.30-37 to 30-40, 1975

[9] C. J. Weinstein, "A Linear Predictive Vocoder with Voice Excitation", Proc. Eascon, September 1975

[10] Auditory toolbox: http://rvl4.ecn.purdue.edu/~malcolm/interval/1998-010/

[11] COLEA: Software Tool for Speech Analysis: http://www.utdallas.edu/~loizou/speech/colea.htm

[12] Orsak, G.C. et al. "Collaborative SP education using the Internet and MATLAB" IEEE SIGNAL PROCESSING MAGAZINE Nov. 1995. vol.12, no.6, pp.23-32.

8 Appendix

The Matlab-code used can be found in this section. The first file is the main file in section 8.1, which is executed. It calls other files to code and decode the sentences.

Two different vocoders are used. The speechcoder1 is the plain LPC vocoder part and the speechcoder2 is the voice excited one. The same code in section 8.2 is used to generate the LPC parameters for both implementations, however, we just use part of them, different inputs, in each vocoder synthesizer. The first synthesizer located in section 8.3.2 uses the pitch and the voiced / unvoiced switch information. The second synthesizer in section 8.4.2 uses the information generated by the errors compressed using a DCT, quantized and decoded. These DCT coding and decoding steps are in the main speechcoder2.m file, which is in 8.4.1. The LPC generation and the synthesizer are based on previously written code [12], somehow modified and adapted to our project.

8.1 Main file

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EE214A - Digital Speech Processing - Class Project, Winter 2002
%
% Speech Coding using Linear Predictive Coding (LPC)
%
% Author: Philipp Steurer, 03/04/2002
%
% Project team: Daniel Thell, Ozgu Ozun, Philipp Steurer
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc; % clear the command line
clear all; % clear the workspace

%
% system constants
% ---------------
InputFilename = 's2omwb.wav';

[inspeech, Fs, bits] = wavread(InputFilename); % read the wavefile

outspeech1 = speechcoder1(inspeech);
outspeech2 = speechcoder2(inspeech);

% display the results
figure(1);
subplot(3,1,1);
plot(inspeech);
grid;
subplot(3,1,2);
plot(outspeech1);
grid;
subplot(3,1,3);
plot(outspeech2);
grid;

disp('Press a key to play the original sound!');
pause;
soundsc(inspeech, Fs);

disp('Press a key to play the LPC compressed sound!');
pause;
soundsc(outspeech1, Fs);

disp('Press a key to play the voice-excited LPC compressed sound!');
pause;
soundsc(outspeech2, Fs);

8.2 LPC output information generation

function [aCoeff,resid,pitch,G,parcor,stream] = proclpc(data,sr,L,fr,fs,preemp)
% USAGE: [aCoeff,resid,pitch,G,parcor,stream] = proclpc(data,sr,L,fr,fs,preemp)
%
% This function computes the LPC (linear-predictive coding) coefficients that
% describe a speech signal. The LPC coefficients are a short-time measure of
% the speech signal which describe the signal as the output of an all-pole
% filter. This all-pole filter provides a good description of the speech
% articulators; thus LPC analysis is often used in speech recognition and
% speech coding systems. The LPC parameters are recalculated, by default in
% this implementation, every 20ms.
%
% The results of LPC analysis are a new representation of the signal
% s(n) = G e(n) - sum from 1 to L a(i)s(n-i)
% where s(n) is the original data. a(i) and e(n) are the outputs of the LPC
% analysis with a(i) representing the LPC model. The e(n) term represents
% either the speech source's excitation, or the residual: the details of the
% signal that are not captured by the LPC coefficients. The G factor is a
% gain term.
%
% LPC analysis is performed on a monaural sound vector (data) which has been
% sampled at a sampling rate of "sr". The following optional parameters modify
% the behaviour of this algorithm.
% L - The order of the analysis. There are L+1 LPC coefficients in the output
% array aCoeff for each frame of data. L defaults to 13.
% fr - Frame time increment, in ms. The LPC analysis is done starting every
% fr ms in time. Defaults to 20ms (50 LPC vectors a second)
% fs - Frame size in ms. The LPC analysis is done by windowing the speech
% data with a rectangular window that is fs ms long. Defaults to 30ms
% preemp - This variable is the epsilon in a digital one-zero filter which
% serves to preemphasize the speech signal and compensate for the 6dB
% per octave rolloff in the radiation function. Defaults to .9378.
%
% The output variables from this function are
% aCoeff - The LPC analysis results, a(i). One column of L numbers for each
% frame of data
% resid - The LPC residual, e(n). One column of sr*fs samples representing
% the excitation or residual of the LPC filter.
% pitch - A frame-by-frame estimate of the pitch of the signal, calculated
% by finding the peak in the residual's autocorrelation for each frame.
% G - The LPC gain for each frame.
% parcor - The parcor coefficients. The parcor coefficients give the ratio
% between adjacent sections in a tubular model of the speech
% articulators. There are L parcor coefficients for each frame of
% speech.
% stream - The LPC analysis' residual or excitation signal as one long vector.
% Overlapping frames of the resid output combined into a new one-
% dimensional signal and post-filtered.
%
% The synlpc routine inverts this transform and returns the original speech
% signal.
%
% This code was graciously provided by:
% Delores Etter (University of Colorado, Boulder) and
% Professor Geoffrey Orsak (Southern Methodist University)
% It was first published in
% Orsak, G.C. et al. "Collaborative SP education using the Internet and
% MATLAB" IEEE SIGNAL PROCESSING MAGAZINE Nov. 1995. vol.12, no.6, pp.
% 23-32.
% Modified and debugging plots added by Kate Nguyen and Malcolm Slaney

% A more complete set of routines for LPC analysis can be found at
% http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html

% (c) 1998 Interval Research Corporation

if (nargin<3), L = 13; end
if (nargin<4), fr = 20; end
if (nargin<5), fs = 30; end
if (nargin<6), preemp = .9378; end

[row col] = size(data);
if col==1 data=data'; end

nframe = 0;
msfr = round(sr/1000*fr); % Convert ms to samples
msfs = round(sr/1000*fs); % Convert ms to samples
duration = length(data);
speech = filter([1 -preemp], 1, data)'; % Preemphasize speech
msoverlap = msfs - msfr;
ramp = [0:1/(msoverlap-1):1]'; % Compute part of window

for frameIndex=1:msfr:duration-msfs+1 % frame rate=20ms
frameData = speech(frameIndex:(frameIndex+msfs-1)); % frame size=30ms
nframe = nframe+1;
autoCor = xcorr(frameData); % Compute the cross correlation
autoCorVec = autoCor(msfs+[0:L]);

% Levinson's method
err(1) = autoCorVec(1);
k(1) = 0;
A = [];
for index=1:L
numerator = [1 A.']*autoCorVec(index+1:-1:2);
denominator = -1*err(index);
k(index) = numerator/denominator; % PARCOR coeffs
A = [A+k(index)*flipud(A); k(index)];
err(index+1) = (1-k(index)^2)*err(index);
end

aCoeff(:,nframe) = [1; A];
parcor(:,nframe) = k';

% Calculate the filter
% response
% by evaluating the
% z-transform
if 0
gain=0;
cft=0:(1/255):1;
for index=1:L
gain = gain + aCoeff(index,nframe)*exp(-i*2*pi*cft).^index;
end
gain = abs(1./gain);
spec(:,nframe) = 20*log10(gain(1:128))';
plot(20*log10(gain));
title(nframe);
drawnow;
end

% Calculate the filter response
% from the filter's impulse
% response (to check above).
if 0
impulseResponse = filter(1, aCoeff(:,nframe), [1 zeros(1,255)]);
freqResp = 20*log10(abs(fft(impulseResponse)));
plot(freqResp);
end

errSig = filter([1 A'],1,frameData); % find excitation noise

G(nframe) = sqrt(err(L+1)); % gain
autoCorErr = xcorr(errSig); % calculate pitch & voicing information
[B,I] = sort(autoCorErr);
num = length(I);
if B(num-1) > .01*B(num)
pitch(nframe) = abs(I(num) - I(num-1));
else
pitch(nframe) = 0;
end

% calculate additional info to improve the compressed sound quality
resid(:,nframe) = errSig/G(nframe);
if(frameIndex==1) % add residual frames using a trapezoidal window
stream = resid(1:msfr,nframe);
else
stream = [stream;
overlap+resid(1:msoverlap,nframe).*ramp;
resid(msoverlap+1:msfr,nframe)];
end
if(frameIndex+msfr+msfs-1 > duration)
stream = [stream; resid(msfr+1:msfs,nframe)];
else
overlap = resid(msfr+1:msfs,nframe).*flipud(ramp);
end
end
stream = filter(1, [1 -preemp], stream)';

8.3 Plain LPC vocoder

8.3.1 Main file

function [ outspeech ] = speechcoder( inspeech )

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% EE214A - Digital Speech Processing - Class Project, Winter 2002
%
% Speech Coding using Linear Predictive Coding (LPC)
% The desired order can be selected in the system constants section.
% For the excitation impulse-trains are used. The result does not sound very
% well but with this solution it is possible to achieve a low bitrate!
%
% Author: Philipp Steurer, 03/04/2002
%
% Parameters:
% inspeech : wave data with sampling rate Fs
% (Fs can be changed underneath if necessary)
%
% Returns:
% outspeech : wave data with sampling rate Fs
% (coded and resynthesized)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
% arguments check
% ---------------
if ( nargin ~= 1)
error('argument check failed');
end;

%
% system constants
% ----------------
Fs = 16000; % sampling rate in Hertz (Hz)
Order = 10; % order of the model used by LPC

%
% main
% ----

% encoded the speech using LPC
[aCoeff, resid, pitch, G, parcor, stream] = proclpc(inspeech, Fs, Order);

% decode/synthesize speech using LPC and impulse-trains as excitation
outspeech = synlpc1(aCoeff, pitch, Fs, G);

8.3.2 Plain LPC decoder

function synWave = synlpc(aCoeff,pitch,sr,G,fr,fs,preemp)
% USAGE: synWave = synlpc(aCoeff,pitch,sr,G,fr,fs,preemp);
%
% This function synthesizes a (speech) signal based on a LPC (linear-
% predictive coding) model of the signal. The LPC coefficients are a
% short-time measure of the speech signal which describe the signal as the
% output of an all-pole filter. This all-pole filter provides a good
% description of the speech articulators; thus LPC analysis is often used in
% speech recognition and speech coding systems. The LPC analysis is done
% using the proclpc routine. This routine can be used to verify that the
% LPC analysis produces the correct answer, or as a synthesis stage after
% first modifying the LPC model.
%
% The results of LPC analysis are a new representation of the signal
% s(n) = G e(n) - sum from 1 to L a(i)s(n-i)
% where s(n) is the original data. a(i) and e(n) are the outputs of the LPC
% analysis with a(i) representing the LPC model. The e(n) term represents
% either the speech source's excitation, or the residual: the details of the
% signal that are not captured by the LPC coefficients. The G factor is a
% gain term.
%
% LPC synthesis produces a monaural sound vector (synWave) which is
% sampled at a sampling rate of "sr". The following parameters are mandatory
% aCoeff - The LPC analysis results, a(i). One column of L+1 numbers for each
% frame of data. The number of rows of aCoeff determines L.
% G - The LPC gain for each frame.
% pitch - A frame-by-frame estimate of the pitch of the signal, calculated
% by finding the peak in the residual's autocorrelation for each frame.
%
% The following parameters are optional and default to the indicated values.
% fr - Frame time increment, in ms. The LPC analysis is done starting every
% fr ms in time. Defaults to 20ms (50 LPC vectors a second)
% fs - Frame size in ms. The LPC analysis is done by windowing the speech
% data with a rectangular window that is fs ms long. Defaults to 30ms
% preemp - This variable is the epsilon in a digital one-zero filter which
% serves to preemphasize the speech signal and compensate for the 6dB
% per octave rolloff in the radiation function. Defaults to .9378.
%
% This code was graciously provided by:
% Delores Etter (University of Colorado, Boulder) and
% Professor Geoffrey Orsak (Southern Methodist University)
% It was first published in
% Orsak, G.C. et al. "Collaborative SP education using the Internet and
% MATLAB" IEEE SIGNAL PROCESSING MAGAZINE Nov. 1995. vol.12, no.6, pp.
% 23-32.
% Modifications by Philipp Steurer:
% Using impulse-trains for the voice excitation.

% (c) 1998 Interval Research Corporation
% A more complete set of routines for LPC analysis can be found at
% http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html

if (nargin < 5), fr = 20; end;
if (nargin < 6), fs = 30; end;
if (nargin < 7), preemp = .9378; end;

msfs = round(sr*fs/1000); % framesize in samples
msfr = round(sr*fr/1000); % framerate in samples
msoverlap = msfs - msfr;
ramp = [0:1/(msoverlap-1):1]';
[L1 nframe] = size(aCoeff); % L1 = 1+number of LPC coeffs

for frameIndex=1:nframe
A = aCoeff(:,frameIndex);
% first check if it is voiced or unvoiced sound:
if ( pitch(frameIndex) ~= 0 )
t = 0 : 1/sr : fs*10^(-3); % sr sample freq. for fr ms
d = 0 : 1/pitch(frameIndex) : 1; % 1/pitchfreq. repetition freq.
residFrame = (pulstran(t, d, 'tripuls', 0.001))'; % sawtooth width of 0.001s
residFrame = residFrame + 0.01*randn(msfs+1,1);
else
residFrame = [];
for m = 1:msfs
residFrame = [residFrame; randn];
end % for
end;

synFrame = filter(G(frameIndex), A', residFrame); % synthesize speech from LPC coeffs
if(frameIndex==1) % add synthesize frames using a trapezoidal window
synWave = synFrame(1:msfr);
else
synWave = [synWave; overlap+synFrame(1:msoverlap).*ramp; ...
synFrame(msoverlap+1:msfr)];
end
if(frameIndex==nframe)
synWave = [synWave; synFrame(msfr+1:msfs)];
else
overlap = synFrame(msfr+1:msfs).*flipud(ramp);
end
end;

synWave = filter(1, [1 -preemp], synWave);

8.4 Voice-excited LPC vocoder

8.4.1 Main File

function [ outspeech ] = speechcoder( inspeech )
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% EE214A - Digital Speech Processing - Class Project, Winter 2002
%
% Speech Coding using Linear Predictive Coding (LPC)
% The desired order can be selected in the system constants section.
% For the excitation the residual signal is used. In order to decrease the
% bitrate, the residual signal is discrete cosine transformed and then
% compressed. This means only the first 50 coefficients of the DCT are kept.
% While most of the energy of the signal is stored there, we don't lose a lot
% of information.
%
% Author: Philipp Steurer, 03/05/2002
%
% Parameters:
% inspeech : wave data with sampling rate Fs
% (Fs can be changed underneath if necessary)
%
% Returns:
% outspeech : wave data with sampling rate Fs
% (coded and resynthesized)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
% arguments check
% ---------------
if ( nargin ~= 1)
error('argument check failed');
end;

%
% system constants
% ----------------
Fs = 16000; % sampling rate in Hertz (Hz)
Order = 10; % order of the model used by LPC

%
% main
% ----

% encoded the speech using LPC
[aCoeff, resid, pitch, G, parcor, stream] = proclpc(inspeech, Fs, Order);

% perform a discrete cosine transform on the residual
resid = dct(resid);
[a,b] = size(resid);
% only use the first 50 DCT-coefficients this can be done
% because most of the energy of the signal is conserved in these coeffs
resid = [ resid(1:50,:); zeros(430,b) ];

% quantize the data
resid = uencode(resid,4);
resid = udecode(resid,4);

% perform an inverse DCT
resid = idct(resid);

% add some noise to the signal to make it sound better
noise = [ zeros(50,b); 0.01*randn(430,b) ];
resid = resid + noise;

% decode/synthesize speech using LPC and the compressed residual as excitation
outspeech = synlpc2(aCoeff, resid, Fs, G);

8.4.2 Voice-excited LPC decoder

function synWave = synlpc(aCoeff,source,sr,G,fr,fs,preemp)
% USAGE: synWave = synlpc(aCoeff,source,sr,G,fr,fs,preemp);
%
% This function synthesizes a (speech) signal based on a LPC (linear-
% predictive coding) model of the signal. The LPC coefficients are a
% short-time measure of the speech signal which describe the signal as the
% output of an all-pole filter. This all-pole filter provides a good
% description of the speech articulators; thus LPC analysis is often used in
% speech recognition and speech coding systems. The LPC analysis is done
% using the proclpc routine. This routine can be used to verify that the
% LPC analysis produces the correct answer, or as a synthesis stage after
% first modifying the LPC model.
%
% The results of LPC analysis are a new representation of the signal
% s(n) = G e(n) - sum from 1 to L a(i)s(n-i)
% where s(n) is the original data. a(i) and e(n) are the outputs of the LPC
% analysis with a(i) representing the LPC model. The e(n) term represents
% either the speech source's excitation, or the residual: the details of the
% signal that are not captured by the LPC coefficients. The G factor is a
% gain term.
%
% LPC synthesis produces a monaural sound vector (synWave) which is
% sampled at a sampling rate of "sr". The following parameters are mandatory
% aCoeff - The LPC analysis results, a(i). One column of L+1 numbers for each
% frame of data. The number of rows of aCoeff determines L.
% source - The LPC residual, e(n). One column of sr*fs samples representing
% the excitation or residual of the LPC filter.
% G - The LPC gain for each frame.
%
% The following parameters are optional and default to the indicated values.
% fr - Frame time increment, in ms. The LPC analysis is done starting every
% fr ms in time. Defaults to 20ms (50 LPC vectors a second)
% fs - Frame size in ms. The LPC analysis is done by windowing the speech
% data with a rectangular window that is fs ms long. Defaults to 30ms
% preemp - This variable is the epsilon in a digital one-zero filter which
% serves to preemphasize the speech signal and compensate for the 6dB
% per octave rolloff in the radiation function. Defaults to .9378.
%
% Minor modifications: Philipp Steurer
%
% This code was graciously provided by:
% Delores Etter (University of Colorado, Boulder) and
% Professor Geoffrey Orsak (Southern Methodist University)
% It was first published in
% Orsak, G.C. et al. "Collaborative SP education using the Internet and
% MATLAB" IEEE SIGNAL PROCESSING MAGAZINE Nov. 1995. vol.12, no.6, pp.
% 23-32.
% Modified and debugging plots added by Kate Nguyen and Malcolm Slaney

% (c) 1998 Interval Research Corporation
% A more complete set of routines for LPC analysis can be found at
% http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html

if (nargin < 5), fr = 20; end;
if (nargin < 6), fs = 30; end;
if (nargin < 7), preemp = .9378; end;

msfs = round(sr*fs/1000);
msfr = round(sr*fr/1000);
msoverlap = msfs - msfr;
ramp = [0:1/(msoverlap-1):1]';
[L1 nframe] = size(aCoeff); % L1 = 1+number of LPC coeffs

[row col] = size(source);
if(row==1 | col==1) % continous stream; must be windowed
postFilter = 0; duration = length(source); frameIndex = 1;
for sampleIndex=1:msfr:duration-msfs+1
resid(:,frameIndex) = source(sampleIndex:(sampleIndex+msfs-1))';
frameIndex = frameIndex+1;
end
else
postFilter = 1; resid = source;
end

[row col] = size(resid);
if col<nframe
nframe=col;
end

for frameIndex=1:nframe
A = aCoeff(:,frameIndex);
residFrame = resid(:,frameIndex)*G(frameIndex);
synFrame = filter(1, A', residFrame); % synthesize speech from LPC coeffs

if(frameIndex==1) % add synthesized frames using a trapezoidal window
synWave = synFrame(1:msfr);
else
synWave = [synWave; overlap+synFrame(1:msoverlap).*ramp; ...
synFrame(msoverlap+1:msfr)];
end
if(frameIndex==nframe)
synWave = [synWave; synFrame(msfr+1:msfs)];
else
overlap = synFrame(msfr+1:msfs).*flipud(ramp);
end
end;

if(postFilter)
synWave = filter(1, [1 -preemp], synWave);
end