Digital Systems: Hardware Organization and Design Speech Coding 11/15/2018 Speech Processing Speech Coding Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Speech Coding Definition: Speech Coding is a process that leads to the representation of analog waveforms with sequences of binary digits. Even though availability of high-bandwidth communication channels has increased, speech coding for bit reduction has retained its importance. Reduced bit-rates transmissions is required for cellular networks Voice over IP Coded speech Is less sensitive than analog signals to transmission noise Easier to: protect against (bit) errors Encrypt Multiplex, and Packetize Typical Scenario depicted in next slide (Figure 12.1) 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Telephone Communication System Digital Systems: Hardware Organization and Design 11/15/2018 Digital Telephone Communication System 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Categorization of Speech Coders Digital Systems: Hardware Organization and Design 11/15/2018 Categorization of Speech Coders Waveform Coders: Used to quantize speech samples directly and operate at high-bit rates in the range of 16-64 kbps (bps - bits per second) Vocoders Largely model-based and operate at a low bit rate range of 1.2-4.8 kbps. Tend to be of lower quality than waveform and hybrid coders. Hybrid Coders Are partially waveform coders and partly speech model-based coders and operate in the mid bit rate range of 2.4-16 kbps. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quality Measurements Quality of coding is viewed as the closeness of the processed speech to the original speech or some other desired speech waveform: Naturalness Degree of background artifacts Intelligibility Speaker identifiability Etc. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quality Measurements Subjective Measurement: Diagnostic Rhyme Test (DRT) measures intelligibility. Diagnostic Acceptability Measure and Mean Opinion Score (MOS) test provide a more complete quality judgment. Objective Measurement: Segmental Signal to Noise Ratio (SNR) – average SNR over a short-time segments Articulation Index – relies on an average SNR across frequency bands. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quality Measurements A more complete list and definition of subjective and objective measures can be found at: J.R. Deller, J.G. Proakis, and J.H.I Hansen, “Discrete-Time Processing of Speech”, Macmillan Publishing Co., New York, NY, 1993 S.R. Quackenbush, T.P. Barnwell, and M.A. Clements, “Objective Measures of Speech Quality. Prentice Hall, Englewood Cliffs, NJ. 1988 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Sampling and Reconstruction of Signals 15 November 2018 Veton Këpuska

Analog-to-Digital Conversion. Continuous Signal . Sampled signal with sampling period T satisfying Nyquist rate as specified by Sampling Theorem. Digital sequence obtained after sampling and quantization 15 November 2018 Veton Këpuska

Digital-to-Analog Conversion. Processed digital signal y[n]. Continuous signal representation ya(nT). Low-pass filtered continuous signal y(t). 15 November 2018 Veton Këpuska

Statistical Models for Quantization 15 November 2018 Veton Këpuska

Digital Systems: Hardware Organization and Design 11/15/2018 Statistical Models Speech waveform is viewed as a random process. Various estimates are important from this statistical perspective: Probability density Mean, Variance and autocorrelation One approach to estimate a probability density function (pdf) of x[n] is through histogram. Count up the number of occurrences of the value of each speech sample in pre-defined different ranges: for many speech samples over a long time duration. Normalize the area of the resulting curve to unity. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Statistical Models The histogram of speech (Davenport, Paez & Glisson) was shown to approximate a gamma density: where x is the standard deviation of the pdf. Simpler approximation is given by the Laplacian pdf of the form: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 PDF of Speech 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

PDF Models of Speech 15 November 2018 Veton Këpuska

Example of Distributions GAMMA DISTRIBUTION LAPLACIAN DISTRIBUTION 15 November 2018 Veton Këpuska

Example of Distributions GAUSSIAN DISTRIBUTION where x – in above relations is Standard Deviation. 15 November 2018 Veton Këpuska

Scalar Quantization 15 November 2018 Veton Këpuska

Digital Systems: Hardware Organization and Design 11/15/2018 Scalar Quantization Assume that a sequence x[n] was obtained from speech waveform that has been lowpass-filtered and sampled at a suitable rate with infinite amplitude precision. x[n] samples are quantized to a finite set of amplitudes denoted by . Associated with the quantizer is a quantization step size. Quantization allows the amplitudes to be represented by finite set of bit patterns – symbols. Encoding: Mapping of to a finite set of symbols. This mapping yields a sequence of codewords denoted by c[n] (Figure 12.3a). Decoding – Inverse process whereby transmitted sequence of codewords c’[n] is transformed back to a sequence of quantized samples (Figure 12.3b). 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Scalar Quantization 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Fundamentals Assume a signal amplitude is quantized into M levels. Quantizer operator is denoted by Q(x); Thus Where denotes M possible reconstruction levels – quantization levels, and 1≤i≤M xi denotes M+1 possible decision levels with 0≤i≤M If xi-1< x[n] < xi, then x[n] is quantized to the reconstruction level is quantized sample of x[n]. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Fundamentals Scalar Quantization Example: Assume there M=4 reconstruction levels. Amplitude of the input signal x[n] falls in the range of [0,1] Decision levels and Reconstruction levels are equally spaced: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Figure 12.4 in the next slide. Fundamentals M=4 Decision levels are (?) [0,1/4,1/2,3/4,1] Reconstruction levels assumed to be (?) [0,1/8,3/8,5/8,7/8] Figure 12.4 in the next slide. 15 November 2018 Veton Këpuska

11 10 01 00 15 November 2018 Veton Këpuska

Example of Uniform 2-bit Quantizer Digital Systems: Hardware Organization and Design 11/15/2018 Example of Uniform 2-bit Quantizer 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Uniform Quantizer A uniform quantizer is one whose decision and reconstruction levels are uniformly spaced. Specifically:  is the step size equal to the spacing between two consecutive decision levels which is the same spacing between two consecutive reconstruction levels (Exercise 12.1). Each reconstruction level is attached a symbol – the codeword. Binary numbers typically used to represent the quantized samples (Figure 12.4). 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Example 2.2 Assume there are L = 16 reconstruction levels. Assuming that input values fall within the range [xmin=-1, xmax=1] and that the each value in this range is equally likely. Decision levels and reconstruction levels are equally spaced; D=Di,= (xmax-xmin)/L i=0, …, L.-1, Decision Levels: Reconstruction Levels: 15 November 2018 Veton Këpuska

Example 15 November 2018 Veton Këpuska

Digital Systems: Hardware Organization and Design 11/15/2018 Uniform Quantizer Codebook: Collection of codewords. In general with B-bit binary codebook there are 2B different quantization (or reconstruction) levels. Bit rate is defined as the number of bits B per sample multiplied by sample rate fs: I=Bfs Decoder inverts the coder operation taking the codeword back to a quantized amplitude value (e.g., 01 → ). Often the goal of speech coding/decoding is to maintain the bit rate as low as possible while maintaining a required level of quality. Because sampling rate is fixed for most applications this goal implies that the bit rate be reduced by decreasing the number of bits per sample 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Uniform Quantizer Designing a uniform scalar quantizer requires knowledge of the maximum value of the sequence. Typically the range of the speech signal is expressed in terms of the standard deviation of the signal. Specifically, it is often assumed that: -4x≤x[n]≤4x where x is signal’s standard deviation. Under the assumption that speech samples obey Laplacian pdf there are approximately 0.35% of speech samples fall outside of the range: -4x≤x[n]≤4x. Assume B-bit binary codebook ⇒ 2B. Maximum signal value xmax = 4x. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Uniform Quantizer For the uniform quantization step size  we get: Quantization step size  relates directly to the notion of quantization noise. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Noise Two classes of quantization noise: Granular Distortion Overload Distortion x[n] unquantized signal and e[n] is the quantization noise. For given step size  the magnitude of the quantization noise e[n] can be no greater than /2, that is: Figure 12.5 depicts this property were: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Noise 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Noise Overload Distortion Maximum-value constant: xmax = 4x (-4x≤x[n]≤4x) For Laplacian pdf, 0.35% of the speech samples fall outside the range of the quantizer. Clipped samples incur a quantization error in excess of /2. Due to the small number of clipped samples it is common to neglect the infrequent large errors in theoretical calculations. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Noise Statistical Model of Quantization Noise Desired approach in analyzing the quantization error in numerous applications. Quantization error is considered an ergodic white-noise random process. The autocorrelation function of such a process is expressed as: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error Previous expression states that the process is uncorrelated. Furthermore, it is also assumed that the quantization noise and the input signal are uncorrelated, i.e., E(x[n]e[n+m])=0,  m. Final assumption is that the pdf of the quantization noise is uniform over the quantization interval: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error Stated assumptions are not always valid. Consider a slowly varying – linearly varying signal ⇒ then e[n] is also changing linearly and is signal dependent (see Figure 12.5 in the previous slide). Correlated quantization noise can be annoying. When quantization step  is small then assumptions for the noise being uncorrelated with itself and the signal are roughly valid when the signal fluctuates rapidly among all quantization levels. Quantization error approaches a white-noise process with an impulsive autocorrelation and flat spectrum. One can force e[n] to be white-noise and uncorrelated with x[n] by adding white-noise to x[n] prior to quantization. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Example For the periodic sine-wave signal use 3-bit and 8-bit quantizer values. The input periodic signal is given with the following expression: MATLAB fix function is used to simulate quantization. The following figure depicts the result of the analysis. 15 November 2018 Veton Këpuska

Example Plot a) represents sequence x[n] with infinite precision, b) represents quantized version , c) represents quantization error e[n] for B=3 bits (L=8 quantization levels), and d) is quantization error for B=8 bits (L=256 quantization levels). 15 November 2018 Veton Këpuska

Example (3.1415926535 …) x[n] = p xi-1< x[n] < xi e.g., xi-1=3 & xi=4; xi-1=3.1 & xi=3.2; xi-1=3.14 & xi=3.15; xi-1=3.141 & xi=3.142; xi-1=3.1415 & xi=3.1416; xi-1=3.14159 & xi=3.14160; xi-1=3.141592 & xi=3.141593; xi-1=3.1415926 & xi=3.1415927; xi-1=3.14159265 & xi=3.14159266; xi-1=3.141592653 & xi=3.141592654; xi-1=3.1415926535 & xi=3.1415926536; 15 November 2018 Veton Këpuska

First 10,000 digits of pi: 15 November 2018 Veton Këpuska 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 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4610126483 6999892256 9596881592 0560010165 5256375678 15 November 2018 Veton Këpuska

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error Process of adding white noise is known as Dithering. This decorrelation technique was shown to be useful not only in improving the perceptual quality of the quantization noise but also with image signals. Signal-to-Noise Ratio A measure to quantify severity of the quantization noise. Relates the strength of the signal to the strength of the quantization noise. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error SNR is defined as: Given assumptions for Quantizer range: 2xmax, and Quantization interval: = 2xmax/2B, for a B-bit quantizer Uniform pdf, it can be shown that (see Exercise 12.2): 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error Thus SNR can be expressed as: Or in decibels (dB) as: Because xmax = 4x, then SNR(dB)≈6B-7.2 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Quantization Error Presented quantization scheme is called pulse code modulation (PCM). B-bits per sample are transmitted as a codeword. Advantages of this scheme: It is instantaneous (no coding delay) Independent of the signal content (voice, music, etc.) Disadvantages: It requires minimum of 11 bits per sample to achieve “toll quality” (equivalent to a typical telephone quality) For 10000 Hz sampling rate, the required bit rate is: B=(11 bits/sample)x(10000 samples/sec)=110,000 bps=110 kbps For CD quality signal with sample rate of 20000 Hz and 16-bits/sample, SNR(dB) =96-7.2=88.8 dB and bit rate of 320 kbps. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Nonuniform Quantization 15 November 2018 Veton Këpuska

Nonuniform Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Nonuniform Quantization Uniform quantization may not be optimal (SNR can not be as small as possible for certain number of decision and reconstruction levels) Consider for example speech signal for which x[n] is much more likely to be in one particular region than in other (low values occurring much more often than the high values). This implies that decision and reconstruction levels are not being utilized effectively with uniform intervals over xmax. A Nonuniform quantization that is optimal (in a least-squared error sense) for a particular pdf is referred to as the Max quantizer. Example of a nonuniform quantizer is given in the figure in the next slide. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Nonuniform Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Nonuniform Quantization 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Nonuniform Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Nonuniform Quantization Max Quantizer Problem Definition: For a random variable x with a known pdf, find the set of M quantizer levels that minimizes the quantization error. Therefore, finding the decision and boundary levels xi and xi, respectively, that minimizes the mean-squared error (MSE) distortion measure: D=E[(x-x)2] E-denotes expected value and x is the quantized version of x. It turns out that optimal decision level xk is given by: ^ ^ ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Nonuniform Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Nonuniform Quantization Max Quantizer (cont.) The optimal reconstruction level xk is the centroid of px(x) over the interval xk-1≤ x ≤xk: It is interpreted as the mean value of x over interval xk-1≤ x ≤xk for the normalized pdf p(x). Solving last two equations for xk and xk is a nonlinear problem in these two variables. Iterative solution which requires obtaining pdf (can be difficult). ^ ~ ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Nonuniform Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Nonuniform Quantization 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Companding Alternative to the nonuniform quantizer is companding. It is based on the fact that uniform quantizer is optimal for a uniform pdf. Thus if a nonlinearity is applied to the waveform x[n] to form a new sequence g[n] whose pdf is uniform then Uniform quantizer can be applied to g[n] to obtain g[n], as depicted in the Figure 12.10 in the next slide. ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Companding 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Companding A number of other nonlinear approximations of nonlinear transformation that achieves uniform density are used in practice which do not require pdf measurement. Specifically and A-law and –law companding. -law coding is give by: CCITT international standard coder at 64 kbps is an example application of -law coding. -law transformation followed by 7-bit uniform quantization giving toll quality speech. Equivalent quality of straight uniform quantization achieved by 11 bits. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Adaptive Coding Nonuniform quantizers are optimal for a long term pdf of speech signal. However, considering that speech is a highly-time-varying signal, one has to question if a single pdf derived from a long-time speech waveform is a reasonable assumption. Changes in the speech waveform: Temporal and spectral variations due to transitions from unvoiced to voiced speech, Rapid volume changes. Approach: Estimate a short-time pdf derived over 20-40 msec intervals. Short-time pdf estimates are more accurately described by a Gaussian pdf regardless of the speech class. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Adaptive Coding A pdf derived from a short-time speech segment more accurately represents the speech nonstationarity. One approach is to assume a pdf of a specific shape in particular a Gaussian with unknown variance 2. Measure the local variance then adapt a nonuniform quantizer to the resulting local pdf. This approach is referred to as adaptive quantization. For a Gaussian we have: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Adaptive Coding Measure the variance x2 of a sequence x[n] and use resulting pdf to design optimal max quantizer. Note that a change in the variance simply scales the time signal: If E(x2[n]) = x2 then E[(x [n])2] = 2x2 Need to design only one nonuniform quantizer with unity variance and scale decision and reconstruction levels according to a particular variance. Fix the quantizer and apply a time-varying gain to the signal according to the estimated variance (scale the signal to match the quantizer). 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Adaptive Coding 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Adaptive Coding There are two possible approaches for estimation of a time-varying variance 2[n]: Feed-forward method (shown in Figure 12.11) where the variance (or gain) estimate is obtained from the input Feed-back method where the estimate is obtained from a quantizer output. Advantage – no need to transmit extra side information (quantized variance) Disadvantage – additional sensitivity to transmission errors in codewords. Adaptive quantizers can achieve higher SNR than the use of –law companding. –law companding is generally preferred for high-rate waveform coding because of its lower background noise when transmission channel is idle. Adaptive quantization is useful in variety of other coding schemes. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Presented methods are examples of instantaneous quantization. Those approaches do not take advantage of the fact that speech, music, … is highly correlated signal: Short-time (10-15 samples), as well as Long-time (over a pitch period) In this section methods that exploit short-time correlation will be investigated. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Short-time Correlation: Neighboring samples are “self-similar”, that is, not changing too rapidly from one another. Difference of adjacent samples should have a lower variance than the variance of the signal itself. This difference, thus, would make a more effective use of quantization levels: Higher SNR for fixed number of quantization levels. Predicting the next sample from previous ones (finding the best prediction coefficients to yield a minimum mean-squared prediction error  same methodology as in LPC of Chapter 5). Two approaches: Have a fixed prediction filter to reflect the average local correlation of the signal. Allow predictor to short-time adapt to the signal’s local correlation. Requires transmission of quantized prediction coefficients as well as the prediction error. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Illustration of a particular error encoding scheme presented in the Figure 12.12 of the next slide. In this scheme the following sequences are required: x[n] – prediction of the input sample x[n]; This is the output of the predictor P(z) whose input is a quantized version of the input signal x[n], i.e., x[n] r[n] – prediction error signal; residual r[n] – quantized prediction error signal. This approach is sometimes referred to as residual coding. ~ ^ ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Quantizer in the previous scheme can be of any type: Fixed Adaptive Uniform Nonuniform Whatever the case is, the parameter of the quantizer are determined so that to match variance of r[n]. Differential quantization can also be applied to: Speech, Music, … signal Parameters that represent speech, music, …: LPC – linear prediction coefficients Cepstral coefficients obtained from Homomorphic filtering. Sinewave parameters, etc. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Consider quantization error of the quantized residual: From Figure 12.12 we express the quantized input x[n] as: ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Quantized signal samples differ form the input only by the quantization error er[n]. Since the er[n] is the quantization error of the residual: ⇒ If the prediction of the signal is accurate then the variance of r[n] will be smaller than the variance of x[n] ⇒ A quantizer with a given number of levels can be adjusted to give a smaller quantization error than would be possible when quantizing the signal directly. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization The differential coder of Figure 12.12 is referred to: Differential PCM (DPCM) when used with a fixed predictor and fixed quantization. Adaptive Differential PCM (ADPCM) when used with Adaptive prediction (i.e., adapting the predictor to local correlation) Adaptive quantization (i.e., adapting the quantizer to the local variance of r[n]) ADPCM yields greatest gains in SNR for a fixed bit rate. The international coding standard CCITT, G.721 with toll quality speech at 32 kbps (8000 samples/sec x 4 bits/sample) has been designed based on ADPCM techniques. To achieve higher quality with lower rates it is required to: Rely on speech model-based techniques and The exploiting of long-time prediction, as well as Short-time prediction 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Important variation of the differential quantization scheme of Figure 12.12. Prediction has assumed an all-pole model (autoregressive model). In this model signal value is predicted from its past samples: Any error in a codeword due to for example bit errors over a degraded channel propagate over considerable time during decoding. Such error propagation is severe when the signal values represent speech model parameters computed frame-by frame (as opposed to sample-by-sample). Alternative approach is to use a finite-order moving-average predictor derived from the residual. One common approach of the use of the moving-average predictor is illustrated in Figure 12.13 in the next slide. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Differential and Residual Quantization Digital Systems: Hardware Organization and Design 11/15/2018 Differential and Residual Quantization Coder Stage of the system in Figure 12.13: Residual as the difference of the true value and the value predicted from the moving average of K quantized residuals: p[k] – coefficients of P(z) Decoder Stage: Predicted value is given by: Error propagation is thus limited to only K samples (or K analysis frames for the case of model parameters) 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation Goal - Estimate : filter coefficients {a1, a2, …,ap}; for a particular order p, and A, Over a short time span of speech signal (typically 20 ms) for which the signal is considered quasi-stationary. Use linear prediction method: Each speech sample is approximated as a linear combination of past speech samples ⇒ Set of analysis techniques for estimating parameters of the all-pole model. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation Consider z-transform of the vocal tract model: Which can be transformed into: In time domain it can be written as: Referred to us as a autoregressive (AR) model. Current Sample Input Past Samples Scaling Factor – Linear Prediction Coefficients 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation Method used to predict current sample from linear combination of past samples is called linear prediction analysis. LPC – Quantization of linear prediction coefficients or of a transformed version of these coefficients is called linear prediction coding For ug[n]=0 This observation motivates the analysis technique of linear prediction. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Model Estimation: Definitions Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation: Definitions A linear predictor of order p is defined by: Estimate of s[n] Estimate of ak z 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Model Estimation: Definitions Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation: Definitions Prediction error sequence is given as difference of the original sequence and its prediction: Associated prediction error filter is defined as: If {k}={ak} s[n] P[z] e[n]=Aug[n] ˜ A(z) 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Model Estimation: Definitions Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation: Definitions Note 1: Input sequence Aug[n] can be recovered by passing s[n] through A(z). For the condition that ak ≈ ak the prediction error filter A(z) is called the inverse filter. s[n] Aug[n] 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Model Estimation: Definitions Recovery of s[n]: s[n] is Periodic Speech, and ak = ak , e[n] is impulse train (Aug[n]) and zero most of the time . Aug[n] s[n] 15 November 2018 Veton Këpuska

Model Estimation: Definitions Digital Systems: Hardware Organization and Design 11/15/2018 Model Estimation: Definitions Note 2: If Vocal tract contains finite number of poles and no zeros, Prediction order is correct, then {k}={ak}, and e[n] is an impulse train for voiced speech and for impulse speech e[n] will be just an impulse. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Model Estimation: Definitions Note 3: In a stochastic context, when Aug[n] is white noise, then the inverse filter “whitens” the input signal 15 November 2018 Veton Këpuska

Digital Systems: Hardware Organization and Design 11/15/2018 Example 5.1 Consider an exponentially decaying impulse response of the form h[n]=anu[n] where u[n] is the unit step. Response to the scaled unit sample A[n] is: Consider the prediction of s[n] using a linear predictor of order p=1. It is a good fit since: Prediction error sequence with 1=a is: The prediction of the signal is exact except at the time origin. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Important question is: how to derive an estimate of the prediction coefficients ak, for a particular order p, that would be optimal in some sense. Optimality is measured based on a criteria. An appropriate measure of optimality is mean-squared error (MSE). Goal is to minimize the mean-squared prediction error: E defined as: In reality, a model must be valid over some short-time interval, say M samples on either side of n: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Thus in practice MSE is time-depended and is formed over a finite interval as depicted in previous figure. [n-M,n+M] – prediction error interval. Alternatively: where 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Determine {k} for which En is minimal: Which results in: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Last equation can be rewritten by multiplying through: Define the function: Which gives the following: Referred to as the normal equations given in the matrix form bellow: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization The minimum error for the optimal solution can be derived as follows: Last term in the equation above can be rewritten as: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Thus error can be expressed as: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Remarks: Order (p) of the actual underlying all-pole transfer function is not known. Order can be estimated by observing the fact that a pth order predictor in theory equals that of a (p+1) order predictor. Also predictor coefficients for k>p equal zero (or in practice close to zero and model only noise-random effects). Prediction error en[m] is non-zero only “in the vicinity” of the time n: [n-M,n+M]. In predicating values of the short-time sequence sn[m], p –values outside of the prediction error interval [n-M,n+M] are required. Covariance method – uses values outside the interval to predict values inside the interval Autocorrelation Method – assumes that speech samples are zero outside the interval. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Error Minimization Matrix formulation Projection Theorem: Columns of Sn – basis vectors Error vector en is orthogonal to each basis vector: SnTen=0; where Orthogonality leads to: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method for LP 15 November 2018 Veton Këpuska

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method In previous section we have described a general method of linear prediction that uses samples outside the prediction error interval referred to as covariance method. Alternative approach that does not consider samples outside analysis interval, referred to as autocorrelation method, and will be presented next. This method is: Suboptimal, however it Leads to an efficient and stable solution to normal equations. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Assumes that the samples outside the time interval [n-M,n+M] are all zero, and Extends the prediction error interval, i.e., the range over which we minimize the mean-squared error to ±∞. Conventions: Short-time interval: [n, n+Nw-1] where Nw=2M+1 (Note: it is not centered around sample n as in previous derivation). Segment is shifted to the left by n samples so that the first nonzero sample falls at m=0. This operation is equivalent to: Shifting of speech sequence s[m] by n-samples to the left and Windowing by Nw -point rectangular window: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Windowed sequence can be expressed as: This operation can be depicted in the figure presented on the right. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Important observations that are consequence of zeroing the signal outside of interval: Prediction error is nonzero only in the interval [0,Nw+p-1] Nw-window length p-the predictor order The prediction error is largest at the left and right ends of the segment. This is due to edge effects caused by the way the prediction is done: from zeros – from the left of the window to zeros – from the right of the window 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method To compensate for edge effects typically tapered window is used (e.g., Hamming). Removes the possibility that the mean-squared error be dominated by end (edge) effects. Data becomes distorted hence biasing estimates: k. Let the mean-squared prediction error be given by: Limits of summation refer to new time origin, and Prediction error outside this interval is zero. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Normal equations take the following form (Exercise 5.1): where 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Due to summation limits depicted in the figure on the right function n[i,k] can be written as: Recognizing that only samples in the interval [i,k+Nw-1] contribute to the sum, and Changing variable m⇒ m-i: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Since the above expression is only function of difference i-k thus we denote it as: Letting =i-k, referred to as correlation “lag”, leads to short-time autocorrelation function: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method rn[]=sn[]*sn[-] Autocorrelation method leads to computation of the short-time sequence sn[m] convolved with itself flipped in time. Autocorrelation function is a measure of the “self-similarity” of the signal at different lags . When rn[] is large then signal samples spaced by  are said to by highly correlated. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Properties of rn[]: For an N-point sequence, rn[] is zero outside the interval [-(N-1),N-1]. rn[] is even function of  rn[0] ≥ rn[] rn[0] – energy of sn[m] ⇒ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method If sn[m] is a segment of a periodic sequence, then rn[] is periodic-like with the same period: Because sn[m] is short-time, the overlapping data in the correlation decreases as  increases ⇒ Amplitude of rn[] decreases as  increases; With rectangular window the envelope of rn[] decreases linearly. If sn[m] is a random white noise sequence, then rn[] is impulse-like, reflecting self-similarity only within a small neighborhood. 15 November 2018 Veton Këpuska

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Letting n[i,k] = rn[i-k], normal equation take the form: The expression represents p linear equations with p unknowns, k for 1≤k≤p. Using the normal equation solution, it can be shown that the corresponding minimum mean-squared prediction error is given by: Matrix form representation of normal equations: Rn=rn. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Autocorrelation Method Digital Systems: Hardware Organization and Design 11/15/2018 Autocorrelation Method Expanded form: The Rn matrix is Toepliz: Symmetric about the diagonal All elements of the diagonal are equal. Matrix is (always) invertible A Toeplitz matrix can be decomposed in O(n2) time Implies efficient solution. Rn  rn 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Example 5.3 Consider a system with an exponentially decaying impulse response of the form h[n] = anu[n], with u[n] being the unit step function. Estimate a using the autocorrelation method of linear prediction. h[n] A[n] s[n] Z 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Example 5.3 Apply N-point rectangular window [0,N-1] at n=0. Compute r0[0] and r0[1]. Using normal equations: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Example 5.3 Minimum squared error (from slide 33) is thus (Exercise 5.5): For 1st order predictor, as in this example here, prediction error sequence for the true predictor (i.e., 1 = a) is given by: e[n]=s[n]-as[n-1]=[n] (see example 5.1 presented earlier). Thus the prediction of the signal is exact except at the time origin. This example illustrates that with enough data the autocorrelation method yields a solution close to the true single-pole model for an impulse input. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization 15 November 2018 Veton Këpuska

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) Investigation of scalar quantization techniques was the topic of previous sections. A generalization of scalar quantization referred to as vector quantization is investigated in this section. In vector quantization a block of scalars are coded as a vector rather than individually. An optimal quantization strategy can be derived based on a mean-squared error distortion metric as with scalar quantization. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) Motivation Assume the vocal tract transfer function is characterized by only two resonance's thus requiring four reflection coefficients. Furthermore, suppose that the vocal tract can take on only one of possible four shapes. This implies that there exist only four possible sets of the four reflection coefficients as illustrated in Figure 12.14 in the next slide. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Scalar Quantization – considers each of the reflection coefficient individually: Each coefficient can take on 4 different values ⇒ 2 bits required to encode each coefficient. For 4 reflection coefficients it is required 4x2=8 bits per analysis frame to code the vocal tract transfer function. Vector Quantization – since there are only four possible vocal tract positions of the vocal tract corresponding to only four possible vectors of reflection coefficients. Scalar values of each vector are highly correlated. Thus 2 bits are required to encode the 4 reflection coefficients. Note: if scalars were independent of each other treating them together as a vector would have no advantage over treating them individually. 15 November 2018 Veton Këpuska

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) Consider a vector of N continuous scalars: With VQ, the vector x is mapped into another N-dimensional vector x: Vector x is chosen from M possible reconstruction (quantization) levels: ^ ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) T T 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) VQ-vector quantization operator ri-M possible reconstruction levels for 1≤i<M Ci-ith “cell” or cell boundary If x is in the cell Ci, then x is mapped to ri. ri – codeword {ri} – set of all codewords; codebook. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Vector Quantization (VQ) Digital Systems: Hardware Organization and Design 11/15/2018 Vector Quantization (VQ) Properties of VQ: P1: In vector quantization a cell can have an arbitrary size and shape. In scalar quantization a “cell” (region between two decision levels) can have an arbitrary size, but its shape is fixed. P2: Similarly to scalar quantization, distortion measure D(x,x), is a measure of dissimilarity or error between x and x. ^ ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 VQ Distortion Measure Vector quantization noise is represented by the vector e: The distortion is the average of the sum of squares of scalar components: For the multi-dimensional pdf px(x): 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 VQ Distortion Measure Goal to minimize: Two conditions formulated by Lim: C1: A vector x must be quantized to a reconstruction level ri that gives the smallest distortion between x and ri. C2: Each reconstruction level ri must be the centroid of the corresponding decision region (cell Ci) Condition C1 implies that given the reconstruction levels we can quantize without explicit need for the cell boundaries. To quantize a given vector the reconstruction level is found which minimizes its distortion. This process requires a large search – active area of research. Condition C2 specifies how to obtain a reconstruction level from the selected cell. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 VQ Distortion Measure Stated 2 conditions provide the basis for iterative solution of how to obtain VQ codebook. Start with initial estimate of ri. Apply condition 1 by which all the vectors from a set that get quantized by ri can be determined. Apply second condition to obtain a new estimate of the reconstruction levels (i.e., centroid of each cell) Problem with this approach is that it requires estimation of joint pdf of all x in order to compute the distortion measure and the multi-dimensional centroid. Solution: k-means algorithm (Lloyd for 1-D and Forgy for multi-D). 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 k-Means Algorithm Compute the ensemble average D as: xk are the training vectors and xk are the quantized vectors. Pick an initial guess at the reconstruction levels {ri} For each xk select closest ri. Set of all xk nearest to ri forms a cluster (see Figure 12.16) – “clustering algorithm”. Compute the mean of xk in each cluster which gives a new ri’s. Calculate D. Stop when the change in D over two consecutive interactions is insignificant. This algorithm converges to a local minimum of D. ^ 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 k-Means Algorithm 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

ClusteringUsingGaussianMixtureModelsExample 15 November 2018 Veton Këpuska

Neural Networks Based Clustering Algorithms Digital Systems: Hardware Organization and Design 11/15/2018 Neural Networks Based Clustering Algorithms Kohonen’s SOFM Topological Ordering of the SOFM Offers potential for further reduction in bit rate. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Example of SOFM 15 November 2018 Veton Këpuska

Example of SOFM SOMDemo\SOMDemo\executable\SOMDemo.exe 15 November 2018 Veton Këpuska

SOFM 15 November 2018 Veton Këpuska

SPFM Weights 15 November 2018 Veton Këpuska

Use of VQ in Speech Transmission Digital Systems: Hardware Organization and Design 11/15/2018 Use of VQ in Speech Transmission Obtain the VQ codebook from the training vectors - all transmitters and receivers must have identical copies of VQ codebook. Analysis procedure generates a vector xi. Transmitter sends the index of the centroid ri of the closest cluster for the given vector xi. This step involves search. Receiving end decodes the information by accessing the codeword of the received index and performing synthesis operation. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 Model-Based Coding The purpose of model-based speech coding is to increase the bit efficiency to achieve either: Higher quality for the same bit rate or Lower bit rate for the same quality. Chronological perspective of model-based coding starting with: All-pole speech representation used for coding: Scalar Quantization Vector Quantization Mixed Excitation Linear Prediction (MELP) coder: Remove deficiencies in binary source representation. Code-excited Linear Prediction (CELP) coder: Does nor require explicit multi-band decision and source characterization as MELP. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Recall the basic speech production model of the form: where the predictor polynomial is given as: Suppose: Linear Prediction analysis performed at 100 frames/s 13 parameters are used: 10 all-pole spectrum parameters, Pitch Voicing decision Gain Resulting in 1300 parameters/s. Compared to telephone quality signal: 4000 Hz bandwidth  8000 samples/s (8 bit per sample). 1300 parameters/s < 8000 samples/s 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Instead of prediction coefficients ai use: Corresponding poles bi Partial Correlation Coefficients ki (PARCOR) Reflection Coefficients ri, or Other equivalent representation. Behavior of prediction coefficients is difficult to characterize: Large dynamic range ( large variance) Quantization errors can lead to unstable system function at synthesis (poles may move outside the unit circle). Alternative equivalent representations: Have a limited dynamic range Can be easily enforced to give stability because |bi|<1 and |ki|<1. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Many ways to code linear prediction parameters: Ideally optimal quantization uses the Max quantizer based on known or estimated pdf’s of each parameter. Example of 7200 bps coding: Voice/Unvoiced Decision: 1 bit (on or off) Pitch (if voiced): 6 bits (uniform) Gain: 5 bits (nonuniform) Each Pole bi: 10 bits (nonuniform) 5 bits for bandwidth 5 bits for center frequency Total of 6 poles 100 frames/s 1+6+5+6x10=72 bits Quality limited by simple impulse/noise excitation model. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Improvements possible based on replacement of poles with PARCOR. Higher order PARCOR have pdf’s closer to Gaussian centered around zero  nonuniform quantization. Companding is effective with PARCOR: Transformed pdf’s close to uniform. Original PARCOR coefficients do not have a good spectral sensitivity (change in spectrum with a change in spectral parameters that is desired to minimize). Empirical finding that a more desirable transformation in this sense is to use logarithm of the vocal tract area function ratio: 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Parameters gi: Have a pdf close to uniform Smaller spectral sensitivity than PARCOR: The all pole spectrum changes less with a change in gi than with a change in ki Note that spectrum changes less with the change in ki than with the change in pole positions. Typically these parameters can be coded at 5-6 bits each (significant improvement over 10 bits): 100 frames/s Order 6 of the predictor (6 poles) (1+6+5+6x6)x100 bps = 4800 bps Same quality as 7200 bps by coding pole positions for telephone bandwidth speech. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Basic Linear Prediction Coder (LPC) Digital Systems: Hardware Organization and Design 11/15/2018 Basic Linear Prediction Coder (LPC) Government standard for secure communications using 2.4 kbps for about a decade used this basic LPC scheme at 50 frames per second. Demand for higher quality standards opened up research on two primary problems with speech codes base on all-pole linear prediction analysis: Inadequacy of the basic source/filter speech production model Restrictions of one-dimensional scalar quantization techniques to account for possible parameter correlation. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 A VQ LPC Coder K-means algorithm VQ based LPC PARCOR coder. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 A VQ LPC Coder Use VQ LPC Coder to achieve same quality of speech with lower bit-rate: 10—bit code book (1024 codewords) 800 bps  2400 bps of scalar quantization 44.4 frames/s 440 bits to code PARCOR coefficients per second. 8 bits per frame for: Pitch Gain Voicing 1 bit for frame synchronization per second. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

A VQ LPC Coder Maintain 2400 bps bit rate with a higher quality of speech coding (early 1980): 22-bit codebook  222 = 4200000 codewords. Problems: Intractable solution due to computational requirements (large VQ search) Memory (large Codebook size) VQ based spectrum characterized by a “wobble” due to LPC-based spectrum being quantized: Spectral representation near cell boundary  “wobble” to and from neighboring cells  insufficient number of codebooks. Emphasis changed from improved VQ of the spectrum and better excitation models ultimately to a return to VQ on the excitation. 15 November 2018 Veton Këpuska

Mixed Excitation LPC (MELP) Digital Systems: Hardware Organization and Design 11/15/2018 Mixed Excitation LPC (MELP) Multi-band voicing decision (introduced as a concept in Section 12.5.2 – not covered in slides) Addresses shortcomings of conventional linear prediction analysis/synthesis: Realistic excitation signal Time varying vocal tract formant bandwidths Production principles of the “anomalous” voice. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Mixed Excitation LPC (MELP) Digital Systems: Hardware Organization and Design 11/15/2018 Mixed Excitation LPC (MELP) Model: Different mixtures of impulses and noise are generated in different frequency bands (4-10 bands) The impulse train and noise in the MELP model are each passed through time-varying spectral shaping filters and are added together to form a full-band signal. MELP unique components: An auditory-based approach to multi-band voicing estimation for the mixed impulse/noise excitation. Aperiodic impulses due to pitch jitter, the creaky voice, and the diplophonic voice. Time-varying resonance bandwidth within a pitch period accounting for nonlinear source/system interaction and introducing the truncation effects. More accurate shape of the glottal flow velocity source. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Mixed Excitation LPC (MELP) Digital Systems: Hardware Organization and Design 11/15/2018 Mixed Excitation LPC (MELP) 2.4 kbps coder has been implemented based on the MELP model and has been selected as government standard for secure telephone communications. Original version of MELP uses: 34 bits for scalar quantization of the LPC coefficients (Specifically the line spectral frequencies LSFs). 8 bits for gain 7 bits for pitch and overall voicing Uses autocorrelation technique on the lowpass filtered LPC residual. 5-bits to multi-band voicing. 1-bit for the jittery state (aperiodic) flag. 54 bits per 22.5 ms frame  2.4 bps. In actual 2.4 kbs standard greater efficiency is achieved with vector quantization of LSF coefficients. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Mixed Excitation LPC (MELP) Digital Systems: Hardware Organization and Design 11/15/2018 Mixed Excitation LPC (MELP) Line Spectral Frequencies (LSFs) More efficient parameter set for coding the all-pole model of linear prediction. The LSFs for a pth order all-pole model are defined as follows: Two polynomials of order p+1 are created from the pth order inverse filter A(z) according to: LSFs can be coded efficiently and stability of the resulting syntheses filter can be guaranteed when they are quantized. Better quantization and interpolation properties than the corresponding PARCOR coefficients. Disadvantage is the fact that solving for the roots of P(z) and Q(z) can be more computationally intensive than the PARCOR coefficients. Polynomial A(z) is easily recovered from the LSFs (Exercise 12.18). 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Code-Excited Linear Prediction (CELP) Digital Systems: Hardware Organization and Design 11/15/2018 Code-Excited Linear Prediction (CELP) Concept: Basic Idea in CELP is to represent the residual from long-term prediction on each frame by codewords form a VQ generated codebook (as oppose to multi-pulses) On each frame a codeword is chosen from a codebook of residuals such as to minimize the mean-squared error between the synthesized and original speech waveform. The length of a codeword sequence is determined by the analysis frame length. For a 10 ms frame interval split into 2 inner frames of 5 ms each a codeword sequence is 40 samples in duration for an 8000 Hz sampling rate. The residual and long-term predictor is estimated with twice the time resolution (a 5 ms frame) of the short-term predictor (10 ms frame); Excitation is more nonstationary than the vocal tract. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Code-Excited Linear Prediction (CELP) Digital Systems: Hardware Organization and Design 11/15/2018 Code-Excited Linear Prediction (CELP) Two approach to formation of the codebook: Deterministic Stochastic Deterministic codebook – It is formed by applying the k-means clustering algorithm to a large set of residual training vectors. Channel mismatch Stochastic codebook Histogram of the residual from the long-term predictor follows roughly a Gaussian probability pdf. A valid assumption with exception of plosives and voiced/unvoiced transitions. Cumulative distributions are nearly identical to those for white Gaussian random variables  Alternative codebook is constructed of white Gaussian random variables with unit variance. 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

Digital Systems: Hardware Organization and Design 11/15/2018 CELP Coders Variety of government and International standard coders: 1990’s Government standard for secure communications at 4.8 kbps at 4000 Hz bandwidth (Fed-Std1016) uses CELP coder: Three bit rates: 9.6 kbps (multi-pulse) 4.8 kbps (CELP) 2.4 kbps (LPC) Short-time predictor: 30 ms frame interval coded with 34 bits per frame. 10th order vocal tract spectrum from prediction coefficients transformed to LSFs coded nonuniform quantization. Short-term and long-term predictors are estimated in open-loop Residual codewords are determined in closed-loop form. Current international standards use CELP based coding. G.729 G.723.1 15 November 2018 Veton Këpuska Architecture of a Respresentative 32 Bit Processor

END 15 November 2018 Veton Këpuska