Moir, TJBarrett, JF2011-06-092011-06-092003-12-082003-12-08Proceedings- Royal Society of London A, vol.459(2040), pp.2957 - 29761364-5021https://hdl.handle.net/10292/1265A 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.Copyright © The Royal Society 2003. The Royal Society is committed to the widest possible dissemination of research outputs. Authors may deposit a pre-print or a final, accepted manuscript version (post-print) of their article in a repository at any time. Articles more than 12 months old (biological sciences) and 24 months old (physical sciences) are freely available to all. This excludes the Digital Journal Archive (1665-2000).KepstrumComplex cepstrumSmoothingPredictionColoured noiseJournal ArticleOpenAccess10.1098/rspa.2003.1137