11 Spectral Subtraction

pectral subtraction is a method for restoration of the power spectrum 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 usually 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 inbetween 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. However, owing to random variations of noise, spectral subtraction can result in negative estimates of the short-time magnitude or power spectrum. The magnitude and power spectrum are non-negative variables, and any negative estimates of these variables should be mapped into non-negative values. This nonlinear rectification process distorts the distribution of the restored signal. The processing distortion becomes more noticeable as the signal-to-noise ratio decreases. In this chapter, we study spectral subtraction, and the different methods of reducing and removing the processing distortions. S Noise-free signal space After subtraction of the noise mean Noisy signal space