Adding two signals at a certain SNR

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Petru-Daniel Tudosiu 2016-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/315085-adding-two-signals-at-a-certain-snr

编辑： David Goodmanson 2016-12-3

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Hello,

I need to add two signals (one is the noise, the other is the speech) at a certain SNR.

How can I do this?

I found on Mathworks but I do not understand it and I am reluctant to using it

noise = noise / norm(noise) * norm(signal) / 10.0^(0.05*snr);
noisy = signal + noise;

Could you please explain it to me?

Regards,

Dan

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Petru-Daniel Tudosiu 2016-12-2

If I am to reverse the equation of SNR ( SNR = 10*log(sp/np) ) I will obtain sp = np * 10 ^ (0.1*SNR) which I cant "match" to the equation from my question.

David Goodmanson 2016-12-3

编辑：David Goodmanson 2016-12-3

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Hello P-D, the norms of the signal and noise waveforms are are linear quantities, i.e. amplitudes and not squared amplitudes like power would be. For linear quantities the SNR is

SNR = 20*log10(norm(signal)/norm(noise))

which is exactly the same quantity as with the power expression

SNR = 10*log10(norm(signal)^2/norm(noise)^2)

The first expression inverts to the equation you have. That's my take on all this anyway. As you mentioned, it's a good idea to be reluctant to use something you do not understand and not rely overly much on outside commentary that you have not verified, including this one.

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