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I'm trying to add White Gaussian Noise to an audio file. However; the energy of the noise should be 1/10th of that of the signal. My first attempt is as following:

[y,Fs] = audioread('drum.wav');
%sound(y,Fs);
noisy_sig = addnoise(y,10);
sound(noisy_sig,Fs);

function noisy_sig = addnoise( sig , SNRdb )
   sig_power = norm(sig,2) / length(sig);
   % noise power is equal to sigma^2
   sigma2 = sig_power / 10^(SNRdb/10) ;
   noisy_sig = sig + sqrt(sigma2)*randn(size(sig));
end

When I listen the resulting wav, there is no difference between the original and noisy ones. Am I doing something wrong? Any help would be appreciated.

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  • $\begingroup$ So, Is it correct to say x = y + 0.1*randn(length(y),1) ? The energy of the noise signal should be 1/10th of the original signal. $\endgroup$ – Jason Dec 18 '19 at 15:31
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Your problem is how you calculate the signal power. You are calling norm which calculates $\sqrt{\sum_i |x_i|^2}$ but you want to calculate the sum of the squared values and then divide by the length as you do in your code. Try this instead: sig_power = norm(sig)^2 / length(sig);. This line will calculate $\frac{1}{N}\sum_{i=1}^N |x_i|^2$.

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  • $\begingroup$ Sir, without using this function; can I add the noise like that: x = y + sqrt(0.1) *randn(length(y),1) ? Is this a correct way of adding a noise whose energy is 1/10 of the original signal? $\endgroup$ – Jason Dec 18 '19 at 17:03
  • $\begingroup$ That adds noise with variance $0.1$. But from your comment you don't mention anything about y's power. SNR is signal-to-noise ratio so it is the signal and noise power relative to each other. $\endgroup$ – Engineer Dec 18 '19 at 17:07

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