I am trying to analyse the effects of SNR level on my data.
I have a set of signals in frequency domain with
f_min = 0.5GHz and
f_max = 10.5GHz centered at
f_c = 5.5GHz. These are simulated signals and are noisless (ideal data). Using the
awgn function of MATLAB, I add noise of various SNR levels (
SNR = 10, 20, 30, 50 and 60dB) in frequency domain. I now need to add the same level of SNR to their time-domain counterparts.
I came across something which I didn't quite understand. It goes as follows :
SNR_freq is computed from the data over the whole frequency,
while in practice,
SNR_time matched to pulse data and is computed from the peak of the signal magnitude (
A_max) as shown below :
SNR_freq = 10*log10(E/sigma^2)
SNR_time = 20*log10(A_max/sigma)
sigma is the variance of the signal.
what exactly is the relationship between