Extrapolation algorithms for discrete signals with application in spectral estimation

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Extrapolation, Least Squares Method, Parameter Identification, Signal Processing, Spectrum Analysis, Time Series Analysis, Algorithms, Fourier Transformation, Norms, Power Spectra, Prolate Spheroids, Signal To Noise Ratios

Scientific paper

New algorithms useful for extrapolation and spectral estimation of band-limited sequences in one and two dimensions are presented. It is first shown that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least-squares extrapolation. By going to a conjugate gradient algorithm, convergence and other numerical properties are improved. It is noted that for noisy observations these algorithms could be extended by considering a mean-square extrapolation criterion which gives rise to a mean-square extrapolation filter and to a recursive extrapolation filter. Extension of these algorithms is made for problems in which the signal is known to be periodic. A new set of functions called the periodic-discrete prolate spheroidal sequences, analogous to DPSS, are introduced, and their properties are investigated.

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