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Unformatted text preview: 12 Veton Kpuska 27 164bit Level Quantization Example
^ x = Q( x ) = i = xi  x i 1, x + xi 1 ^ xi = i , 2 1 i L 1 i L February 11, 2012 Veton Kpuska 28 Uniform Quantizer A uniform quantizer is one whose decision and reconstruction levels are uniformly spaced. Specifically: xi  x i 1 = , xi + xi 1 ^ xi = , 2 1 i L 1 i L is the step size equal to the spacing between two consecutive decision levels which is the same spacing between two consecutive reconstruction levels. Each reconstruction level is attached a symbol the codeword. Binary numbers typically used to represent the quantized samples (as in Figure 12.4 in previous slide). February 11, 2012 Veton Kpuska 29 Uniform Quantizer Codebook: Collection of codewords. In general with Bbit 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 ^ x2 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 Veton Kpuska 30 February 11, 2012 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: 4xx[n]4x 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: 4xx[n]4x. Assume Bbit binary codebook 2B. Maximum signal value xmax = 4x. February 11, 2012 Veton Kpuska 31 Uniform Quantizer 2( xmax  xmin ) 2 xmax 2x = = 2 B 2 xmax = 2 B = max 2B For the uniform quantization step size we get: Quantization step size relates directly to the notion of quantization noise. February 11, 2012 Veton Kpuska 32 Quantization Noise Two classes of quantization noise: Granular Distortion Granular Distortion Overload Distortion ^ x[n] = x[n] + e[n] 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:  e[ n] 2 2 ^ e[n] = x[n]  x[n]
February 11, 2012 Veton Kpuska 33 Quantization Noise February 11, 2012 Veton Kpuska 34 Example For the periodic sinewave signal use 3bit and 8bit quantizer values. The input periodic signal is given with the following expression: x[ n] = cos( 0 n ) , 0 = 2F0 = 0.76 2 MATLAB fix function is used to simulate quantization. The following figure depicts the result of the analysis. February 11, 2012 Veton Kpuska 35 L=23=8 & 28= 256 Levels Quantization Plot a) represents sequence x[n] with infinite precision, b)...
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