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I previously asked a general question about noise reduction, but none of the answers mentioned this specific method or algorithm. (the noise reduction button on some radios and DSP software seems to enable spectral subtraction, rather than just blanking, etc.)
How does Spectral Subtraction reduce noise in receiver audio? Why does this method or algorithm of noise reduction possibly create the problem of (reportedly) adding musical noise?
From https://link.springer.com/chapter/10.1007/978-3-322-92773-6_9 :
Spectral subtraction is a method for restoration of the power or the magnitude spectrum of a signal observed in additive noise, through subtraction of an estimate of the average noise spectrum from the noisy signal spectrum. The noise spectrum is estimated, and updated, from the periods when the signal is absent and only the noise is present.
The assumption is that the noise is a stationary or a slowly varying process, and that the noise spectrum does not change significantly in-between the update periods. For restoration of time-domain signals, an estimate of the instantaneous magnitude spectrum is combined with the phase of the noisy signal, and then transformed via an inverse discrete Fourier transform to the time domain. In terms of computational complexity spectral subtraction is relatively inexpensive.
The technical description of how spectral subtraction works is described in Mike Waters' answer. I will attempt to describe how it generates musical noise.
Spectral subtraction operates by estimating the long-term average background noise and subtracting it from the audio signal. If the estimated average background noise has peaks in it that do not correspond to the current audio signal, these peaks have nothing to cancel and instead generate musical noise.
