1. Speech Processing Speech Coding

2. 4 June 2016Veton Këpuska2 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)

3. 4 June 2016Veton Këpuska3 Digital Telephone Communication System

4. 4 June 2016Veton Këpuska4 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)  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.  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.

5. 4 June 2016Veton Këpuska5 Quality Measurements  Quality of coding can 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.

6. 4 June 2016Veton Këpuska6 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.

7. 4 June 2016Veton Këpuska7 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

8. 4 June 2016Veton Këpuska8 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 different ranges: for many speech samples over a long time duration. Normalize the area of the resulting curve to unity.

9. 4 June 2016Veton Këpuska9 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:

10. 4 June 2016Veton Këpuska10 PDF of Speech

11. 4 June 2016Veton Këpuska11 PDF Models of Speech

12. 4 June 2016Veton Këpuska12 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).

13. 4 June 2016Veton Këpuska13 Scalar Quantization

14. 4 June 2016Veton Këpuska14 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 x i denotes M+1 possible decision levels with 0≤i≤M  If x i-1 < x[n] < x i, then x[n] is quantized to the reconstruction level  is quantized sample of x[n].

15. 4 June 2016Veton Këpuska15 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:  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.

16. 4 June 2016Veton Këpuska16 Example of Uniform 2-bit Quantizer

17. 4 June 2016Veton Këpuska17 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).

18. 4 June 2016Veton Këpuska18 Uniform Quantizer  Codebook: Collection of codewords.  In general with B-bit binary codebook there are 2 B different quantization (or reconstruction) levels.  Bit rate is defined as the number of bits B per sample multiplied by sample rate f s : I=Bf s  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

19. 4 June 2016Veton Këpuska19 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 ⇒ 2 B. Maximum signal value x max = 4  x.

20. 4 June 2016Veton Këpuska20 Uniform Quantizer  For the uniform quantization step size  we get:  Quantization step size  relates directly to the notion of quantization noise.

21. 4 June 2016Veton Këpuska21 Quantization Noise  Two classes of quantization noise: Granular Distortion Overload Distortion  Granular 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:

22. 4 June 2016Veton Këpuska22 Quantization Noise

23. 4 June 2016Veton Këpuska23 Quantization Noise  Overload Distortion Maximum-value constant:  x max = 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.

24. 4 June 2016Veton Këpuska24 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:

25. 4 June 2016Veton Këpuska25 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:

26. 4 June 2016Veton Këpuska26 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.

27. 4 June 2016Veton Këpuska27 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.

28. 4 June 2016Veton Këpuska28 Quantization Error  SNR is defined as:  Given assumptions for Quantizer range: 2x max, and Quantization interval: = 2x max /2 B, for a B-bit quantizer Uniform pdf, it can be shown that (see Exercise 12.2):

29. 4 June 2016Veton Këpuska29 Quantization Error  Thus SNR can be expressed as:  Or in decibels (dB) as:  Because x max = 4 x, then SNR(dB)≈6B-7.2

30. 4 June 2016Veton Këpuska30 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.

31. 4 June 2016Veton Këpuska31 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 x max.  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.

32. 4 June 2016Veton Këpuska32 Nonuniform Quantization

33. 4 June 2016Veton Këpuska33 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 x i and x i, 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 x k is given by: ^ ^ ^

34. 4 June 2016Veton Këpuska34 Nonuniform Quantization  Max Quantizer (cont.) The optimal reconstruction level x k is the centroid of p x (x) over the interval x k-1 ≤ x ≤x k : It is interpreted as the mean value of x over interval x k-1 ≤ x ≤x k for the normalized pdf p(x). Solving last two equations for x k and x k is a nonlinear problem in these two variables.  Iterative solution which requires obtaining pdf (can be difficult). ^ ~ ^

35. 4 June 2016Veton Këpuska35 Nonuniform Quantization

36. 4 June 2016Veton Këpuska36 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. ^

37. 4 June 2016Veton Këpuska37 Companding

38. 4 June 2016Veton Këpuska38 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.

39. 4 June 2016Veton Këpuska39 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.

40. 4 June 2016Veton Këpuska40 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:

41. 4 June 2016Veton Këpuska41 Adaptive Coding  Measure the variance  x 2 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(x 2 [n]) =  x 2 then E[(x [n]) 2 ] =  2  x 2 1.Need to design only one nonuniform quantizer with unity variance and scale decision and reconstruction levels according to a particular variance. 2.Fix the quantizer and apply a time-varying gain to the signal according to the estimated variance (scale the signal to match the quantizer).

42. 4 June 2016Veton Këpuska42 Adaptive Coding

43. 4 June 2016Veton Këpuska43 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.

44. 4 June 2016Veton Këpuska44 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.

45. 4 June 2016Veton Këpuska45 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: 1.Have a fixed prediction filter to reflect the average local correlation of the signal. 2.Allow predictor to short-time adapt to the signal’s local correlation.  Requires transmission of quantized prediction coefficients as well as the prediction error.

46. 4 June 2016Veton Këpuska46 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. ~ ^ ^

47. 4 June 2016Veton Këpuska47 Differential and Residual Quantization

48. 4 June 2016Veton Këpuska48 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.

49. 4 June 2016Veton Këpuska49 Differential and Residual Quantization  Consider quantization error of the quantized residual:  From Figure 12.12 we express the quantized input x[n] as: ^

50. 4 June 2016Veton Këpuska50 Differential and Residual Quantization  Quantized signal samples differ form the input only by the quantization error e r [n].  Since the e r [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.

51. 4 June 2016Veton Këpuska51 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

52. 4 June 2016Veton Këpuska52 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.

53. 4 June 2016Veton Këpuska53 Differential and Residual Quantization

54. 4 June 2016Veton Këpuska54 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)

55. 4 June 2016Veton Këpuska55 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.

56. 4 June 2016Veton Këpuska56 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. 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.

57. 4 June 2016Veton Këpuska57 Vector Quantization (VQ)

58. 4 June 2016Veton Këpuska58 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: ^ ^

59. 4 June 2016Veton Këpuska59 Vector Quantization (VQ) T T

60. 4 June 2016Veton Këpuska60 Vector Quantization (VQ) VQ-vector quantization operator r i -M possible reconstruction levels for 1≤i<M C i -i th “cell” or cell boundary  If x is in the cell C i, then x is mapped to r i. r i – codeword {r i } – set of all codewords; codebook.

61. 4 June 2016Veton Këpuska61 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 is shape is fixed. P2:Similarly to scalar quantization, distortion measure D(x,x), is a measure of dissimilarity or error between x and x. ^ ^

62. 4 June 2016Veton Këpuska62 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 p x (x):

63. 4 June 2016Veton Këpuska63 VQ Distortion Measure  Goal to minimize:  Two conditions formulated by Lim: C1:A vector x must be quantized to a reconstruction level r i that gives the smallest distortion between x and r i. C2:Each reconstruction level r i must be the centroid of the corresponding decision region (cell C i ) 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.

64. 4 June 2016Veton Këpuska64 VQ Distortion Measure  Stated 2 conditions provide the basis for iterative solution of how to obtain VQ codebook. Start with initial estimate of r i. Apply condition 1 by which all the vectors from a set that get quantized by r i 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).

65. 4 June 2016Veton Këpuska65 k-Means Algorithm 1.Compute the ensemble average D as: x k are the training vectors and x k are the quantized vectors. 2.Pick an initial guess at the reconstruction levels {r i } 3.For each x k select closest r i. Set of all x k nearest to r i forms a cluster (see Figure 12.16) – “clustering algorithm”. 4.Compute the mean of x k in each cluster which gives a new r i ’s. Calculate D. 5.Stop when the change in D over two consecutive interactions is insignificant.  This algorithm converges to a local minimum of D. ^

66. 4 June 2016Veton Këpuska66 k-Means Algorithm

67. 4 June 2016Veton Këpuska67 Neural Networks Based Clustering Algorithms  Kohonen’s SOFM Topological Ordering of the SOFM Offers potential for further reduction in bit rate.

68. 4 June 2016Veton Këpuska68 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 x i.  Transmitter sends the index of the centroid r i of the closest cluster for the given vector x i. This step involves search.  Receiving end decodes the information by accessing the codeword of the received index and performing synthesis operation.

69. 4 June 2016Veton Këpuska69 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.

70. 4 June 2016Veton Këpuska70 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

71. 4 June 2016Veton Këpuska71 Basic Linear Prediction Coder (LPC)  Instead of prediction coefficients a i use: Corresponding poles b i Partial Correlation Coefficients k i (PARCOR) Reflection Coefficients r i, 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 |b i |<1 and |k i |<1.

72. 4 June 2016Veton Këpuska72 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: 1.Voice/Unvoiced Decision: 1 bit (on or off) 2.Pitch (if voiced): 6 bits (uniform) 3.Gain: 5 bits (nonuniform) 4.Each Pole b i : 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.

73. 4 June 2016Veton Këpuska73 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:

74. 4 June 2016Veton Këpuska74 Basic Linear Prediction Coder (LPC)  Parameters g i : Have a pdf close to uniform Smaller spectral sensitivity than PARCOR:  The all pole spectrum changes less with a change in g i than with a change in k i  Note that spectrum changes less with the change in k i 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.

75. 4 June 2016Veton Këpuska75 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: 1.Inadequacy of the basic source/filter speech production model 2.Restrictions of one-dimensional scalar quantization techniques to account for possible parameter correlation.

76. 4 June 2016Veton Këpuska76 A VQ LPC Coder  VQ based LPC PARCOR coder. K-means algorithm

77. 4 June 2016Veton Këpuska77 A VQ LPC Coder 1.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.

78. 4 June 2016Veton Këpuska78 A VQ LPC Coder  Maintain 2400 bps bit rate with a higher quality of speech coding (early 1980):  22-bit codebook  2 22 = 4200000 codewords.  Problems: 1.  Intractable solution due to computational requirements (large VQ search)  Memory (large Codebook size) 2.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.

79. 4 June 2016Veton Këpuska79 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.

80. 4 June 2016Veton Këpuska80 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: 1.An auditory-based approach to multi-band voicing estimation for the mixed impulse/noise excitation. 2.Aperiodic impulses due to pitch jitter, the creaky voice, and the diplophonic voice. 3.Time-varying resonance bandwidth within a pitch period accounting for nonlinear source/system interaction and introducing the truncation effects. 4.More accurate shape of the glottal flow velocity source.

81. 4 June 2016Veton Këpuska81 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.

82. 4 June 2016Veton Këpuska82 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 p th order all-pole model are defined as follows:  Two polynomials of order p+1 are created from the p th 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).

83. 4 June 2016Veton Këpuska83 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.

84. 4 June 2016Veton Këpuska84 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.

85. 4 June 2016Veton Këpuska85 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.  10 th 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