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Linear prediction: Mathematics and engineering. (English) Zbl 0792.94001

Summary: We present an introduction to some aspects of digital signal processing and time series analysis which are not always covered in classical textbooks. One of the objectives is to illustrate how mathematics and engineering can be combined in a fruitful interplay, resulting in many new techniques and methods in many different fields. We illustrate how the prediction problem is related to linear algebra, orthogonal polynomials, classical interpolation problems, inverse scattering theory, Toeplitz operators, network theory etc.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E11 Filtering in stochastic control theory
65F05 Direct numerical methods for linear systems and matrix inversion
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
41A20 Approximation by rational functions
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