uniform-quantizers - EE380 Communication Systems Spring...

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EE380: Communication Systems Spring 2010-2011 Quantization Error and Quantization Noise (For a Uniform Quantizer) Consider a quantizer whose input signal is x ( t ) and the output is the quantized signal y ( t ). Then the quantization error q ( t ) = y ( t ) - x ( t ). For a given sample, we define: q = Y - X . When the probability density function of X is smooth and the number of quantization intervals ( L ) is large, we will find an expression for quantization noise, i.e., power of q ( t ) without assuming that q is a uniform random variable. Let the density function of X is f X ( x ). We define p k as the probability that X lies between x k - 1 and x k (see figure). Note that x k - 1 and x k are the end points of the k -th quantization interval. Whenever X falls within this interval, the output of the quantizer is y k . The corresponding quanti- zation error is y k - X . Clearly, the proba- bility of this error occurring is p k . Δ p (x) X X x x k-1 k k p Thus, the quantization noise (power of the quantization error signal) is given by: N q = L summationdisplay k =1 x k
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