Let = cos 2 be the signal which is undergoing quantization.

Then for this signal, the power will be ** **/2

i.e =

Suppose if we are quantizing a signal with n-bits , then the step size(i.e difference between quantization steps) will be

= =

The maximum quantization error can be q/2. So it is usually assumed that quantization noise is uniformly distributed from -q/2 to q/2. Hence the probability density function is a rectangle with height 1/q and extends it’s base from -q/2 to +q/2. Note that the area under PDF curve should be equal to 1.

Quantization noise power is calculated as follows

= =

Signal to quantization noise ratio is a ratio of signal power to the quantization noise power

SQNR= =1.5 *

= 10 log {1.5 * }

=1.76 +6.02n

For any doubts regarding derivation, please use comment section.

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