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A kepstrum approach to filtering, smoothing and prediction with application to speech enhancement

A kepstrum (or complex–cepstrum) approach to minimum–phase Wiener filtering of stationary scalar processes is proposed and solved for the case of signal plus coloured noise, where the noise possibly includes a white–noise component. A general solution is found in an innovations form. The spectral factorization of the noise model and of the signal–plus–noise model required for the solution are determined from data using the kepstrum technique with the fast Fourier transform. This approach avoids dependence on any form of multidimensional state–space or polynomial–based model and so avoids use of recursive parameter estimation or of Diophantine equations.