Quantization (signal processing): Difference between revisions

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:<math>Q(x) = \frac{\left\lfloor 2^{M-1}x \right\rfloor+0.5}{2^{M-1}}</math>.
 
In this case the <math>f(x)</math> and <math>g(i)</math> operators are just multiplying scale factors (one multiplier being the inverse of the other) along with an offset in ''g''(''i'') function to place the representation value in the middle of the input region for each quantization index. The value <math>2^{-(M-1)}</math> is often referred to as the ''quantization step size''. Using this quantization law and assuming that [[quantization noise]] is approximately [[uniform distribution (continuous)|uniformly distributed]] over the quantization step size (an assumption typically accurate for rapidly varying <math>x</math> or high <math>M</math>) and further assuming that the input signal <math>x</math> to be quantized is approximately uniformly distributed over the entire interval from -1 to 1, the [[signal to noise ratio]] (SNR) of the quantization can be computed as
 
:<math>