Generalisations of maximum-entropy pattern analysis

It is shown that the widely used discrete Fourier transform entails hidden unnecessary and often unrealistic assumptions. The more powerful maximum-entropy method generates an all-pole spectrum avoiding these pitfalls - at the cost of more complex computation - but it too contains certain implicit restrictions. Some of these may be eased by newer methods allowing for spectra with zeros as well as poles. The paper goes onto show that, and broadly how, the maximum-entropy approach may be further developed and generalised to cover an even wider range of situations, patterns and features, including constraints on the source system, observations of nonstationary distributions and known noise powers or characteristics. Finally a formal philosophical basis for generalised pattern analysis and feature extraction is outlined.