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

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Mohamad 2020-11-4

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https://ww2.mathworks.cn/matlabcentral/answers/635760-adding-noise-to-a-signal-and-which-caculation-of-signal-to-noise-ratio-is-correct

评论： Mohamad 2020-11-5

noise_test.mat

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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

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Mathieu NOE 2020-11-4

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uh..

be careful your definition of SNR2 says

% uisng the original signal

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

Mohamad 2020-11-5

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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
    