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How to add Guassian Noise to non sinusoidal signal

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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
.

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Accepted Answer

Ameer Hamza
Ameer Hamza on 10 May 2020
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

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