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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?

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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.

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