we know that signal-to-Noise Ratio is defined as
let is a given signal which is a single tone signal .
The maximum value of RMS signal power is .
Normalized signal power with R=1.
we know that slope overload distortion can be eliminated if and only if .
By substituting value in P then the power results to be .
Quantization Noise Power :-
if uniform (or) linear Quantization is used in DM system, during the approximation process of with there exists some error between these two signals . This error is called as Quantization error (or) noise.
In discrete time domain .
Quantization error = Quantized signal- original signal.
Now to find out Quantization noise , assume it is uniformly distributed random variable
now the Probability density function of this uniformly distributed random variable is
Mean square value of this random variable is with zero mean
simplification gives .
Mean Square value= Quantization Noise Power.
The M signal is passed through a reconstruction Low pass Filter at the output of a DM Receiver . The Band width of this filter is in such a way that .
where is the sampling frequency of the signal.
now assume that Quantization noise is distributed over a frequency band up to and is given by .
then the noise power distributed over will be