Basic audio denoising in the frequency domain using minimum statistics?

Question

I'm trying to do some example elementary denoising of the audio signal. Let's say input is speech with constant traffic background noise.

• First I calculated block-based overlap-add Fourier transform (size 512) and continued in the frequency domain with the signal in[n].
• Then I used minimum statistics method to estimate the noise in the frequency domain noise[n].
• Lastly I calculated the gain[n] as signal-to-noise ratio in[n]/noise[n].

Now that I have gain[n], how should I continue in order to filter the signal and go back to the time domain?

Answer 1

Once you have calculated the gain function in the frequency domain, you can apply it to your noisy signal to obtain a denoised signal. The steps you should follow are:

1- Multiply the noisy signal's Fourier transform by the gain function in the frequency domain. This gives you the processed Fourier coefficients.

2- Take the inverse Fourier transform of the processed Fourier coefficients. This gives you the denoised signal in the time domain.

3- In order to avoid artifacts at the beginning and end of the signal, you should overlap-add the denoised segments using a window function.