Speech Compression using LPC

Speech Compression using LPC

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  Adaptive Signal ProcessingTerm Paper 2015 DISHA MODI (Roll No:15MECC12) 1 Abstract—The past decade has observed progress towards the submission of low-rate speech coders to public and military communications. It is essential to this progress that has been the new speech coders accomplished high quality speech at low data rates. These coders include mechanisms to show the spectral properties of speech like speech waveform matching, and improve the code performance for the human ear. Several of these have been adopted in cellular telephony standards. Service providers are unceasingly met with the challenge of accommodating more users within a limited allocated bandwidth in mobile communication services. For this object, service providers are constantly in search of low bit-rate speech coders that deliver high-quality speech. In this paper the simulated low bit rate speech signal using Linear Predictive Coding (LPC) in MATLAB was implemented. Index Terms—Auto Correlation, Formants, LPC, Levinson Durbin recursion. I. INTRODUCTION ―LPC was first introduced as a method for encoding human speech by the United States Department of Defense in federal standard 1015, published in 1984‖[1]. Vocal tract can be approximated as a variable diameter tube. Human speech is produced in the vocal tract. The linear predictive coding (LPC) model is based on the vocal tract characterized by this tube of a varying diameter and it represented in mathematical approximation. At a particular time, the speech sample is equals to linear sum of the p previous samples. The important facet of LPC is the linear predictive filter which determines the value of the next sample by a linear combination of previous samples. ―In normal scenario, speech is sampled at 8000 samples/second with 8 bits quantization. This delivers data rate of 64000 bits/second. Linear predictive coding drops this to 2400 bits/second.‖[1]. At this rate the speech has a distinct synthetic sound and there is an obvious loss of quality. However, the speech can still be easily understandable and audible to human kind. Hence, it is a lossy form of compression. Sometimes, lossy algorithms are thought-out acceptable because the loss of quality is often undetectable to the human ear. Fact is that in conversations silence take up greater than 50% of time. It is an easy way to save bandwidth that not to transmit the silence. One important thing about speech production is that mechanically there is a high correlation between adjacent samples of speech. II. LPC SYSTEM IMPLEMENTATION The filter model used in LPC is known as the linear predictive filter. It has two key components: analysis / encoding and synthesis / decoding. III. LPC Analyzing/encoding The encoding part of LPC includes observing the speech signal and break down it into segments. Fig. 1 LPC encoder block-diagram LP methods have been used in control and information theory—called methods of system estimation and system identification used extensively in speech under group of names mentioned below referred from [7]. 1. covariance method 2. autocorrelation method 3. lattice method 4. inverse filter formulation 5. spectral estimation formulation 6. maximum likelihood method 7. inner product method A. Input speech Under the normal situation, the input signal is sampled at a rate of 8000 samples per second. This input signal is then break down into segments and it is transmitted to the receiver. The 8000 samples in each second of speech signal are broken into approx. 180 sample segments. This means that each segment represents 22.5 milliseconds of the input speech signal. B. Voice/Unvoiced Determination As per LPC algorithm, before a speech segment is determined as being voiced or unvoiced it is first passed through a low- pass filter with a band of 1 kHz. It is important to determine if a segment is voiced or unvoiced because voiced sounds have a distinct waveform then unvoiced sounds. The LPC encoder informs the decoder if a signal segment is voiced or unvoiced by sending a single bit. Remember that voiced sounds are generally vowels and can be considered as a pulse that is similar to periodic waveforms. These sounds have very large amplitudes and high energy levels. Voiced sounds also have distinct formant or resonant frequencies. Unvoiced sounds are usually non-vowel or consonants sounds and often have random waveforms and are chaotic. It has smaller amplitudes then voiced sounds and therefore less energy. Hence, the decision of voiced and unvoiced speech signals is confirmed by counting the number of times a waveform crosses the x-axis and then comparing that value to the normally range of values (threshold Values) for most unvoiced and voiced sounds. Speech Compression using LPC Disha Modi, M.Tech (Communication), Electronics and Communication Department Institute of Technology - Nirma University
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  Adaptive Signal ProcessingTerm Paper 2015 DISHA MODI (Roll No:15MECC12) 2 C. Pitch Period Estimation The pitch period can be thought of as the period of the vocal cord vibration that happens during the construction of voiced speech. Therefore, the pitch period is only required for the decoding of voiced segments and is not needed for unvoiced segments since they are produced by turbulent air flow not vocal cord vibrations. One type of algorithm takes advantage of the fact that the autocorrelation of a period function, Rxx(k), will have a maximum when k is equivalent to the pitch period. These algorithms usually detect a maximum value by checking the autocorrelation value against a threshold value. One problem with algorithms that use autocorrelation is that the validity of their results is susceptible to interference as a result of other resonances in the vocal tract. When interference occurs the algorithm can’t guarantee accurate results. Another problem with autocorrelation algorithms occurs because voiced speech is not entirely periodic. This means that the maximum will be lower than it should be for a true periodic signal. D. Vocal Tract Filter The filter that is used by the decoder to re-form the original input signal is formed based on a set of coefficients. In order to find the filter coefficients that best match the current segment being examined the encoder tries to minimize the mean squared error. = ∑ E[ ∑ ]=0 -2E[ ∑ ]=0 ∑ [ ] [ ] (Use fact that [ ] Taking the derivative yields a set of M equations. To solve for the filter coefficients E[ ] has to be estimate. Autocorrelation is the approach that will be explained here for linear predictive coding. Autocorrelation needs several initial assumptions be made about the set or sequence of speech samples, [ ], in the current segment. First, it needs [ ] be stationary and second, it needs the [ ] sequence is zero outside of the current segment. In autocorrelation, each E[ ] is converted into an autocorrelation function of the form Ryy(|i-j|). The estimation of an autocorrelation function Ryy(k) can be expressed as follows. Using Ryy(k), the M equations that were acquired from taking the derivative of the mean squared error can be written in matrix form RA = P where A contains the filter coefficients. In order to determine the filter coefficients, the equation A = P must be solved. This equation cannot be solved without first computing . This is an easy computation if one observes that R is symmetric and all diagonals consist of the same element. This type of matrix is called a Toeplitz matrix and can be easily inverted [1]. The Levinson-Durbin (L-D) Algorithm is a recursive algorithm that is considered very computationally efficient since it takes advantage of the properties of R when determining the filter coefficients. L-D Algorithm [2] The basic simple ideas behind the recursion are first that it is easy to solve the system for k =1, and second that it is also very simple to solve for a k +1 coefficients sized problem when we have solved a for a k coefficients sized problem. In general none of the coefficients of the different sized problem match, so it is not a way to calculate but a way to calculate the whole vector as a function of , and . Thinking about it Levinson-Durbin induction would be a better name. We are looking for =[ ] so that =[ ] with =[ ] and is not necessary at this stage. The dot product of the second line of gives + = 0 Therefore, and + Solving the size K+1 Problem Suppose that we have solved the size k problem and have found , and . Then we have has one more row and column than so we cannot apply it directly to , however if we expend with a zero and call this vector we can apply to it and we get the following interesting result
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  Adaptive Signal ProcessingTerm Paper 2015 DISHA MODI (Roll No:15MECC12) 3 Since the matrix is symmetric, we also have something remarkable when reversing the order of coefficients of and calling this vector . We can notice that a linear combination is of the form wanted for since the first element is a 1 for all values of . Now if there was a value of for Calculating ) gives IV. TRANSMITTING THE PARAMETERS[1] In an original form, speech is usually transmitted at 64,000 bits/second using 8 bits/sample and a rate of 8000 Hz for sampling. LPC drops this rate to 2,400 bits/second by breaking the speech into segments and then directing the voiced/unvoiced information, the pitch period, and the coefficients for the filter that signifies the vocal tract for each segment. The compressed signal used by the filter on the receiver end is determined by the classification of the speech segment as voiced or unvoiced and by the pitch period of the segment. The encoder transmits a single bit to tell if the current segment is voiced or unvoiced. The pitch period is quantized using quantizer. 6 bits are required to represent the pitch period. If the segment contains voiced speech than a 10th order filter is used. This means that 11 values are needed: 10 reflection coefficients and the gain. If the segment contains unvoiced speech than a 4th order filter is used. This means that 5 values are needed: 4 reflection coefficients and the gain. Quantization done as follows: 1 bit voiced/unvoiced 6 bits pitch period (60 values) 10 bits k1 and k2 (5 each) 10 bits k3 and k4 (5 each) 16 bits k5, k6, k7, k8 (4 each) 3 bits k9 2 bits k10 5 bits gain G 1 bit synchronization 54 bits TOTAL BITS PER FRAME Verification for Bit Rate of LPC Speech Segments Sample rate = 8000 samples/second Samples per segment = 180 samples/segment Segment rate = Sample Rate/ Samples per Segment = (8000 samples/second)/ (180 samples/second) = 44.444444.... Segments/second Segment size = 54 bits/segment Bit rate = Segment size * Segment rate = (54 bits/segment) * (44.44 segments/second) = 2400 bits/second V. LPC synthesis/decoding Fig. 2 LPC synthesizer/decoder block-diagram [4] The process of decoding a sequence of speech segments is the reverse of the encoding process. Each segment is decoded individually and the sequence of reproduced sound segments is joined together to represent the entire input speech signal. The decoding or synthesis of a speech segment is based on the 54 bits of information that are transmitted from the encoder. Each segment of speech has a different LPC filter that is eventually produced using the reflection coefficients and the gain that are received from the encoder. 10 reflection coefficients are used for voiced segment filters and 4 reflection coefficients are used for unvoiced segments. These reflection coefficients are used to generate the vocal tract coefficients or parameters which are used to create the filter. The final step of decoding a segment of speech is to pass the excitement signal through the filter to produce the synthesized speech signal. VI. APPLICATION In general, the most common usage for speech compression is in standard telephone systems. In fact, a lot of the technology
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  Adaptive Signal ProcessingTerm Paper 2015 DISHA MODI (Roll No:15MECC12) 4 used in speech compression was developed by the phone companies. Further applications of LPC and other speech compression schemes are voice mail systems, telephone answering machines, and multimedia applications. Most multimedia applications, unlike telephone applications, involve one-way communication and involve storing the data. SIMULATION RESULTS Simulated low bit rate different speech signals using Linear Predictive Coding (LPC) in MATLAB was implemented. Fig. 3 Female Original Voice Fig. 4 Female LPC coded Voice Fig. 5 Male Original Voice Fig. 6 Male LPC coded Voice Performance measurements of LPC compressed signals (both male and female) are shown in Table I. Looking at the SNR computed in Table I, it is obvious that both male and female sounds are noisy as they have a low SNR value. It observed that for all levels of compression the quality is better with male signal than female signal; On the other hand the compression factor with female signal has larger values comparable with these of male signal. This result is expected because the female voice has more high frequencies than male voice. It has observed that no further enhancements can be achieved beyond certain level of decomposition for both signals. PARAMETER MALE FEMALE Sampling Rate 8000 8000 File length (in seconds) 2.07 2.77 Length of Original Signal 99328 133120 Length of Constructed Signal 97920 132480 SNR(in dB) 17.077 14.77 Compression Ratio 0.9858 0.9952 Table 1 Comparison of male and female LPC synthesized voice CONCLUSION Linear Predictive Coding is an analysis/synthesis technique to lossy speech compression that attempts to model the human production of sound instead of transmitting an estimate of the sound wave. Linear predictive coding achieves a bit rate of 2400 bits/second which makes it ideal for use in secure telephone systems. Secure telephone systems are more concerned that the content and meaning of speech, rather than the quality of speech, be preserved. The tradeoff for LPC’s low bit rate is that it does have some difficulty with certain sounds and it produces speech that sound synthetic. Linear predictive coding encoders break up a sound signal into different segments and then send information on each segment to the decoder. The encoder send information on whether the segment is voiced or unvoiced and the pitch period for voiced segment which is used to create an excitement signal in the decoder. The encoder also sends information about the vocal tract which is used to build a filter on the decoder side which when given the excitement signal as input can reproduce the original speech. REFERENCES [1] J. Bradbury, ―Linear Predictive Coding,‖ 2000. [2] C. Collomb, ―1 . Description of Linear Prediction 2 . Minimizing the error,‖ pp. 1–7, 2009. [3] D. R. Sandeep, ―Compression and Enhancement of Speech Signals,‖ no. Seiscon, pp. 774–779, 2011. [4] M. A. Osman, N. Al, H. M. Magboub, and S. A. Alfandi, ―Speech compression uses LPC and wavelet,‖ pp. 92–99, 2010. [5] V. Hardman and O. Hodson. Internet/Mbone Audio (2000) 5-7. [6] Scott C. Douglas. Introduction to Adaptive Filters, Digital Signal Processing Handbook (1999) 7-12. [7] D. S. Processing, ―Digital Speech Processing — Lecture 13 Linear Predictive Coding ( LPC ) - Introduction LPC Methods.‖ Poor, H. V., Looney, C. G., Marks II, R. J., Verdú, S., Thomas, J. A., Cover, T. M. Information Theory. The Electrical Engineering Handbook (2000) 56-57.