February 11 2012 veton kpuska 69 differential and

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Unformatted text preview: esonance'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: Vector Quantization since there are only four possible vocal tract positions of the vocal tract corresponding to only four possible vectors of reflection coefficients. 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. 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. February 11, 2012 Veton Kpuska 74 Vector Quantization (VQ) February 11, 2012 Veton Kpuska 75 Vector Quantization (VQ) Consider a vector of N continuous scalars: x = x , x , x ,..., x 1 2 3 [ N T With VQ, the vector x is mapped into another N ^ dimensional vector x: ^ ^ ^ ^ ^ x = x , x , x ,..., x 1 2 3 [ N T ^ Vector x is chosen from M possible reconstruction (quantization) levels: ^ x = VQ[ x] = r i , for x Ci 76 February 11, 2012 Veton Kpuska Vector Quantization (VQ) T T February 11, 2012 Veton Kpuska 77 Vector Quantization (VQ) VQvector quantization operator riM possible reconstruction levels for 1i<M Ciith "cell" or cell boundary ri codeword If x is in the cell Ci, then x is mapped to ri. {ri} set of all codewords; codebook. February 11, 2012 Veton Kpuska 78 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. February 11, 2012 Veton Kpuska 79 VQ Distortion Measure Vector quantization noise is represented by the vector e: ^ e= x-x The distortion is the average of the sum of squares of scalar components: D=Ee e For the multidimensional pdf px(x): ^ ^ D = E ( x - x) ( x - x) = T M T [ T T [ ... ( x^ - x ) - - - ^ ( x - x ) px ( x ) d x = ... ( r i - x ) ( r i - x ) p x ( x ) d x i =1 xCi February 11, 2012 Veton Kpuska 80 VQ Distortion Measure Goal to minimize: T ^ ^ D = E ( x - x) ( x - x) [ 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. Condition...
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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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