Proper way to add noise to signal

Question

In many areas I have found that while adding noise, we mention some specification like zero mean and variance. I need to add AWGN, colored noise, uniform noise of varying SN

Answer 1

You can use randn() to generate a noise vector 'awgnNoise' of the length you want. Then, given a specified SNR value, calculate the power of the orignal signal and the power of the noise vector 'awgnNoise'. Get the right amplitude scaling factor for the noise vector and just scale it.

The following code is an example to corrupt signal with white noise, assuming input signal is 1D and real valued.

function out_signal = addAWGN(signal, targetSNR)
sigLength = length(signal); % length
awgnNoise = randn(size(signal)); % orignal noise
pwrSig = sqrt(sum(signal.^2))/sigLength; % signal power
pwrNoise = sqrt(sum(awgnNoise.^2))/sigLength; % noise power

scaleFactor = (pwrSig/pwrNoise)/targetSNR; %find scale factor
awgnNoise = scaleFactor*awgnNoise; 
out_signal = signal + awgnNoise; % add noise

Be careful about the sqrt(2) factor when you deal with complex signal, if you want to generate the real and imag part separately.