Keywords

1 Introduction

The speech coding is a procedure to represent a digitized speech signal with its minimum bit format necessary to transmit it over different channels. Speech coding is a wide area of research from late 80s to present. The advancement in speech coding techniques is necessary due to rapid increase in users of mobile communication and limited bandwidth of channels. The speech coders are creating a competitive environment between the telecom provider giants; better speech quality with lower bit rates is demanding one. The basic building blocks for speech coders are shown in Fig. 1. The low bit rate and high speech quality are the main requirements to design a speech coder [1, 2]. The speech coders are classified into two terms.

Fig. 1
figure 1

Block diagram of speech coding system

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  1. (a)

    Waveform coders—pulse code modulation (PCM), differential pulse code modulation (DPCM), adaptive differential pulse code modulation (ADPCM).

  2. (b)

    Parametric coders—linear predictive coding (LPC), residual excited linear prediction, mixed excited linear prediction, code excited linear prediction (RELP, MELP, CELP).

2 Literature Survey

The research on speech coding starts at Bell laboratories, and the first electronic voice synthesizer was invented by Homer W. Dudley in 1930 for secure voice transmission during world war. Motivation for speech coding research at that time is to design a system which is bandwidth efficient for telegraph cables. Dudley practically demonstrates the speech and figure out the redundancy in speech and finally set up with the new procedure of analysis by synthesis method for designing of speech coder [3].

The basic idea behind the first coder was to analyze speech in terms of its pitch spectrum by band-pass filter to analyze the periodic and random analysis of speech. The improvement on speech coders had been done during 1940s–1960s [4].

The early vocoder system is totally based upon the analog signal, and the digital representation gains interest because of its best encryption and better fidelity over long-range transmission. In 1940s, a new term introducing the speech coding named as pulse code modulation (PCM). PCM is a direct method for representation of discrete time and discrete amplitude of analog signals. The more advancement in this technique is started, and the best quantization capabilities were developed in differential PCM, delta modulation, and adaptive DPCM were developed and speech coding in PCM with 64 kbps and with ADPCM 32 kbps become the standard of Consultative Committee for International Telephony and Telegraphy (CCITT) [2].

A great innovative invention was done by Prof. Fant in 1950s, the linear speech source system. The mode consists of linear time-varying coefficient of speech signals excited by periodic impulse train for both voiced (speech) and unvoiced (noise) signal, and this model becomes the basic building block for new generation linear predictive speech coding [4, 5].

Theoretical and practical aspect on linear predictive speech coding is analyzed by Markel and Gray in 1970s. In between 1970s and 1980s, the rapid growth in speech coders was done because of drastic boom in VLSI technology.

In the duration on 1980s–1990s, the low rate high-quality speech coders were planned to design. The invention of code excited linear prediction coding was major improvement in speech coders, CELP is originally proposed by M. R. Schroeder and B. S. Atal in 1985. CELP was capable of producing low rate speech for communication purpose [6, 7].

The concept for hybrid code is finalized with the use of different structured codebooks in CELP. An 8 kbps hybrid coder was first hybrid coder which was selected for North American Digital Telephone Network. The hybrid coders are also selected for satellite systems.

The research on this field is still going on and researchers continuously working on to increase the capacity of systems at minimal bandwidth.

3 Linear Predictive Coding

LPC technique is the most used technique in speech coding. LPC technique provides extremely accurate estimates of speech data sequence. Basic idea of linear prediction is that the current speech sample can be closely approximated as a linear combination of past samples, the block diagram for LPC filter is shown in Fig. 2.

Fig. 2
figure 2

Block diagram of linear predictive filter

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The algorithm for LPC is given by the formula given below:

$$ y(n) = \sum\limits_{(i = 1)}^{N} {ay(n - i)} $$
(1)

The efficient estimation of LP coefficients is based on the Levinson–Durbin algorithm which uses a forward and backward prediction for speech samples.

The formula basically used for both forward and backward samples is:

$$ r\left( i \right) = \sum\limits_{n = 0}^{N - 1 - i} { s\left( n \right) \cdot s\left( {n + i} \right)} $$
(2)

where r is a positive-definite matrix

$$ \begin{aligned} & r { = }\left[ {r\left( 1\right) r\left( 2\right) \ldots r\left( {n{ + 1}} \right)} \right] \\ & \left( {\begin{array}{*{20}c} {r1} & {r2} & {r\left( n \right)} \\ {r2} & {r1} & {r\left( {n - 1} \right)} \\ { r\left( n \right)} & {r\left( {n - 1} \right)} & {r1} \\ \end{array} } \right) \left( {\begin{array}{*{20}c} {a1} \\ {a2} \\ { a\left( {n + 1} \right)} \\ \end{array} } \right) = R\left( n \right) \\ \end{aligned} $$
(3)

4 Code Excited Linear Prediction (CELP)

Parametric coding is based on LP analysis, and CELP is standardized as parametric coder by CCITT in 1991 which is formally known as FS1016 CELP [8] and given the bit rate of 4.8 kbps. Advancement in this technique is observed in 1992, and an another big achievement was successfully done by International Telecommunication Union (ITU), and another version of CELP is finalized as ITU-T G.728 LD-CELP with bit rate 16 kbps and abbreviated as low-delay code excited linear predictive coder (LD-CELP) which was designed to provide delay of less than 20 ms.

The block diagram in Fig. 3 shows the basic building block of CELP. In CELP, coder a fixed codebook is designed to provide initial code vectors for data bit comparison and hence the high quality of speech is attained at much lower bit rate then waveform coders; thus, the bandwidth is optimized as compared to waveform coders. The perceptual weighted filter is used to provide a fixed delay for each sample, and it is a constant value in between 0.1 and 0.9.

Fig. 3
figure 3

Block diagram of CELP coder

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5 Evaluation and Analysis

Analysis of 16 and 9.6 kbps CELP is done with the MATLAB simulating software version R2016a. The coder is designed to take audio speech samples at 8 kHz, and output is observed in 16 and 9.6 kbps. The ‘hello’ file is taken as input audio and ‘xhat1’ is decoded sound file in 16 kbps sampled format and ‘xhat2’ is 9.6 kbps decoded sound for CELP. Finally, the experiment is performed for a constant value of c = 0.25 and 0.65. The original sound is standard sound in ITU-T test signal library. The signal sampled in 86,169 samples and the 50 LP coefficients are calculated randomly from 86,169 samples. Fig. 4 shows the LP estimation of original speech. Similarly, Figs. 5 and 6 show the comparison graph between 16 kbps CELP and 9.6 kbps CELP with c = 0.25.

Fig. 4
figure 4

LP coefficient estimate

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Fig. 5
figure 5

Graph between 16 kbps CELP and original speech with c = 0.25

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Fig. 6
figure 6

Graph between 9.6 kbps CELP and original speech with c = 0.25

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6 Performance Comparison

SNR is abbreviated as signal to noise ratio, and MSE is abbreviated as mean square error estimation of speech signals. The two signals ‘xhat1’ (16 kbps) and ‘xhat2’ (9.6 kbps) CELP are compared with ‘hello’ original signal, and values for SNR and MSE are shown in Table 1.

Table 1 SNR and MSE parameters for 16 kbps/9.6 kbps CELP coder
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7 Result and Discussions

Here, a detail performance analysis of 16 kbps CELP and 9.6 kbps CELP with perceptual weighted value c = 0.65 and c = 0.25 is presented. This analysis is totally based on the value of perceptual weighted constant ‘c.’ The factor ‘c’ is highly affecting factor for the quality of speech coders. These simulation-based comparative analyses illustrate the output speech quality in terms of signal to noise ratio (SNR) and mean square error (MSE), and from the comparison, it is clear that lower value of c is needed for better results. In Figs. 7 and 8, the graphical representation for both parameters is shown for various values of c.

Fig. 7
figure 7

SNR of the 16 and 9.6 kbps CELP compared with original

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Fig. 8
figure 8

MSE of the 16 and 9.6 kbps CELP compared with original

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8 Conclusion

From the above experimental test it is clearly analyzed that at lower the value of c better the SNR and similarly at lower values of c MSE is lesser. From both 16 and 9.6 kbps, the ratings for 16 kbps are better than 9.6 kbps. It is clearly shown that at c = 0.25 values for both SNR and MSE among both the better results are considered for 16 kbps CELP.

The 16 kbps CELP is a parametric coder and best for audio speech processing. The exponential growth in telecom field needs a better version of speech and video processing both at same time for real-time implementation so research in this section is continuously growing and better quality of speech or video coder is implemented. The enhance voice services (EVS) and iLBC are example of it [9, 10].