Ri set of all codewords codebook february 11 2012

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Unformatted text preview: C2 specifies how to obtain a reconstruction level from the selected cell. To quantize a given vector the reconstruction level is found which minimizes its distortion. This process requires a large search active area of research. February 11, 2012 Veton Kpuska 81 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 multidimensional centroid. Solution: kmeans algorithm (Lloyd for 1D and Forgy for multi D). February 11, 2012 Veton Kpuska 82 kMeans Algorithm 1. 2. 3. 4. 5. Compute the ensemble average D as: 1 N -1 ^ ^ D = ( x k - x k )T ( x k - x k ) N k =0 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. February 11, 2012 Veton Kpuska 83 kMeans Algorithm February 11, 2012 Veton Kpuska 84 Neural Networks Based Clustering Algorithms Kohonen's SOFM Topological Ordering of the SOFM Offers potential for further reduction in bit rate. February 11, 2012 Veton Kpuska 85 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. Veton Kpuska 86 February 11, 2012 ModelBased Coding The purpose of modelbased 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 modelbased coding starting with: Allpole speech representation used for coding: Mixed Excitation Linear Prediction (MELP) coder: Scalar Quantization Vector Quantization Codeexcited Linear Prediction (CELP) coder: Remove deficiencies in binary source representation. Does nor require explicit multiband decision and source characterization as MELP. Veton Kpuska 87 February 11, 2012 Basic Linear Prediction Coder (LPC) Recall the basic speech production model of the form: A A H ( z)= = A( z ) 1- P( z ) P ( z ) = a k z -k k =1 where the predictor polynomial is given as: p Suppose: Linear Prediction analysis performed at 100 frames/s 13 parameters are used: 10 allpole spectrum parameters, Pitch...
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This note was uploaded on 02/10/2012 for the course ECE 3552 taught by Professor Staff during the Fall '10 term at FIT.

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