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 .

let

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.

(approximation process)

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

.

.

.

.