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In the paper a review is given of modern parametric spectral analysis methods based on difference-equation models, in contrast with classical spectral analysis based on Fourier transform approaches. The algorithms discussed are based on an autoregressive structure as this leads to simple, efficient estimators. To provide fast algorithms, recursion in model order is introduced, while a lattice-filter structure can also assist in improving the speed of certain algorithms. The problem of spectral leakage is considered, with emphasis being given to algorithms which produce fine frequency resolutions with small bias. Recursion in time, which produces a sequential estimation, is described, and gives rise to a range of algorithms ranging from Kalman-filter-type methods to simple LMS algorithms due to Widrow. A wide range of examples is given based on simulated data and biomedical cases.These illustrate the problems caused by initial phase shift in a short time series, but also the considerable improvement in frequency resolution over the FFT approach. The use of parametric spectral analysis in tracking fine frequency fluctuations is illustrated with gastrointestinal electrical activity data.