Example: Spectral subtraction

A speech signal, s, is corrupted by additive noise, n. The combined signal, s+n, is observed and an estimate of the noise amplitude spectrum, is also available. An estimate of the original signal amplitude spectrum, , is given by:
 

That is, the estimated amplitude of the signal at a given frequency is the real amplitude of the signal plus noise at that frequency minus the estimated noise amplitude. The phase of the signal is assumed to be the same as that of the signal plus noise. This modification of the frequency domain information can be placed within the overlap and add framework to give the technique know as spectral subtraction [6, 7].

There are several problems with this method.

• It is quite likely that equation 39 results in a negative estimate of . This is not physical and a simple solution is to set such values to zero.
• There are invariably large differences between and . If then considerable noise remains.
• All channels are processed independently: This often leads to one channel of one frame having a significant spuriously high amplitude. The resulting signal has a short tonal burst and this problem is referred to as that of ``musical tones''.

Lots of fancy tricks (i.e. tweaks) can be added to this basic method, for example the subtraction of an overestimate of the noise signal or the use of median filtering to help suppress the musical tones [6, 7]