How to calculate SNR of signals in MATLAB?

Question

I've encountered a very simple, yet fundamental problem on calculating the SNR:

There are several signals :

• S1 = original and pure clean signal without noise.

• N1 = white Gaussian noise which is going to be added to S1.

• S2 = S1 + N1 (the noisy signal before performing the noise-reduction algorithm)

• S3 = noise-reduced signal (after performing noise reduction algorithm)

• N2 = S3 - S1 (the amount of noise after performing the noise-reduction algorithm)

Now I want to compare the SNR before and after performing the noise-reduction algorithm.

1. Which signals should I consider for SNR_before!? S1/N1 or S2/N1 ?

2. Which signals should I consider for SNR_after!? S3/N1 or S3/N2 ?

3. Which commands or functions should I use in MATLAB in order to compute SNR_before and SNR_after?

Thanks a billion for putting your time on helping me.

Answer 1

What i know about calculating snr before :

snrBeforeNoise = mean( signal .^ 2 ) / mean( noise .^ 2 );

and about snr after :

residual_noise = signal - noise_reduced_signal; snr_after = mean( signal .^ 2 ) / mean( residual_noise .^ 2 );