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I have a sample speech recording with background noise. I managed to extract part of the noise signal, and put the noise and the contaminated signal in the same plot. enter image description here

I have done fft-analysis on both speech and noise, and since their frequency bands with centralized power are close to each other, I cannot simply apply a bandpass filter. Is there another way to remove the noise from the speech signal with knowledge of the noise itself? (No, subtraction does not work)

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    $\begingroup$ Obviously, subtracting can only work for things you know – noise, by nature, is random. $\endgroup$ – Marcus Müller Jun 4 '16 at 10:17
  • $\begingroup$ Do you mean by knowledge of the noise? You said "extract part of the noise signal": where, and how? $\endgroup$ – Laurent Duval Jun 4 '16 at 12:09
  • $\begingroup$ @LaurentDuval There're some parts of the original speech where the person is not talking, so there's only background noise. I extracted that part and extended it to the same length of the original signal. $\endgroup$ – F. Bai Jun 4 '16 at 18:20
  • $\begingroup$ @F. Bai You can check the noise properties on these parts. You might have a deterministic and a random parts, to help you do further processing $\endgroup$ – Laurent Duval Jun 4 '16 at 18:33
  • $\begingroup$ Your question has beeen answered. Do not hesitate to vote for the useful ones and accept the most suitable $\endgroup$ – Laurent Duval Feb 9 '17 at 17:16
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The signal seems non-stationary, at least less stationary than the noise, and the noise is of relatively lower amplitude. Hence, a class of methods resides in performing one or several non-stationary transformations (time-frequency, time-scale, or spectrograms and wavelets). They can concentrate useful signals on a little amount of coefficients. Then, thresholding or shrinkage techniques, reducing low-coefficients and preserving higher ones can be interesting.

Free softwares like audacity have build-in functions. For more techniques, you can check for instance:

More advanced techniques, termed "source separation", are for instance described by:

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Programs such as Adobe Audition (video link) and Izotope RX (video link) are able to reduce noise by a two-step process that goes roughly like this:

  1. Spectrally profile the noise in non-voiced segments of the audio. You can select a suitable segment by yourself. I don't know the details of what kind of statistics are collected at this step.
  2. In the complete audio, reduce the magnitude of the frequency bins depending on the noise profile. I don't know the details of this step either.

Such processing creates artifacts and the programs use different tricks such as spectral smoothing to reduce them. Different material may benefit from using a different FFT size.

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