How to add Guassian Noise to non sinusoidal signal

Hi,

Given a SNR value in dB I want to add noise to my below narrow pulsed signal .

Fs=200e6;

Fs=200e6;
t=t=0:1/Fs:255/Fs;
Fc=50e6;
tau1=400e-9;
tau2=80e-9;
Req_SNR=10; % in dB
Sn= sin(2*pi*Fc*t).*exp(-4*pi*(((t-tau1)/tau2).^2));

I am following below steps to add noise to signal.

Pow_Sn=sum(St.^2);  % compute signal power
rn=randn(1, size(t)); 
rn_power=sum(rn.^2);
Noise_amp=sqrt(Pow_Sn./((10^(Req_SNR/10)))); % 
Noise=rn.*Noise_amp; 
Sn_Noise=Sn+Noise;
SNR_measured=snr(Sn_Noise,Noise); % to test.

My questions are as followings:

1. Is Signal power computation correct.
2. Is noise generation method correct.
3. Why SNR_measured do not equal to Req_SNR.

Note: randn outout are not in range of -3.25 to 3.02

.

Answer 1

[Ameer Hamza]

You are confusing the energy and power of the signal. Calculate the value power of signal like this

Pow_Sn=sum(Sn.^2)/numel(Sn);

Try the following code

Fs=200e6;
t=0:1/Fs:255/Fs;
Fc=50e6;
tau1=400e-9;
tau2=80e-9;
Req_SNR=10; % in dB
Sn= sin(2*pi*Fc*t).*exp(-4*pi*(((t-tau1)/tau2).^2));

Pow_Sn=sum(Sn.^2)/numel(Sn);  % compute signal power
rn=randn(1, numel(t)); 
rn_power=sum(rn.^2);
Noise_amp=sqrt(Pow_Sn./((10^(Req_SNR/10)))); % 
Noise=rn.*Noise_amp; 
Sn_Noise=Sn+Noise;
SNR_measured=snr(Sn,Noise); % to test.

snr requires the clean signal and the noise.

Result:

SNR_measured =
   10.2936