Adding noise to a signal and which caculation of Signal to Noise Ratio is correct ?

Hi , Please I need to add white gaussain noise with a variance = (4/9)*var(sig) to the signal in ( noise_test.mat) .

I need to know which caculation of Signal to Noise Ratio is correct , is it SNR1 or SNR2 ?

Is it ratio of variances of the original signal to Noise or the corrupted signal to Noise ?

    load noise_test.mat
    noise=(2/3)*std(y)*randn(size(y)); %% generate zero-mean white gaussian noise with a variance = (4/9)*var(sig)
    sig=y+noise; % Add generated noise to get the corrupted signal 
    SNR1 = var(y)/var(noise); % caculate ( SNR ) using the corrupted signal 
    SNR2 = var(sig)/var(noise); % caculate (SNR ) uisng the original signal
    SNR1dB=10*log10(SNR1); % caculate noisy ( SNR ) in dB
    SNR2dB=10*log10(SNR2); % caculate noisy ( SNR ) in dB

Thanks

[Mathieu NOE]

hello

IMHO, its the original signal vs noise

A SNR of 0 dB (1) means signal and noise have same power / rms levels

[Mohamad]

Hi , so this is the correct one , right ?

SNR2 = var(sig)/var(noise); % caculate (SNR ) uisng the original signal
SNR2dB=10*log10(SNR2); % caculate noisy ( SNR ) in dB

[Mathieu NOE]

uh..

be careful your definition of SNR2 says

% uisng the original signal

"

whereas you actually use sig in the computation (signal + noise)

[Mohamad]

Ok , I modified , Thanks alot

load noise_test.mat
noise=(2/3)*std(y)*randn(size(y)); %% generate zero-mean white gaussian noise with a variance = (4/9)*var(sig)
sig=y+noise; % Add generated noise to get the corrupted signal 
SNR = var(y)/var(noise); % caculate ( SNR ) using the corrupted signal 
SNRdB=10*log10(SNR); % caculate noisy ( SNR ) in dB