Mathematical Foundations of Signal Processing

Mathematical Foundations of Signal Processing

An operator-theoretic overview of discrete-time single-channel signal processing is given, covering such topics as the time and frequency domain structure of weakly stationary stochastic processes, the design and effect of linear filters, and prediction theory. The ultimate underpinnings of the subj...

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Veröffentlicht in:SIAM review 1979-07, Vol.21 (3), p.361-388
1. Verfasser: Holmes, Richard B.
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Coefficients
Digital filters
Domain analysis
Hilbert space
Hilbert spaces
Linear filters
Mathematical theorems
Numbers
Signal processing
Spectral energy distribution
Stochastic models
Stochastic processes
Theorems
Transfer functions
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Beschreibung
Zusammenfassung:An operator-theoretic overview of discrete-time single-channel signal processing is given, covering such topics as the time and frequency domain structure of weakly stationary stochastic processes, the design and effect of linear filters, and prediction theory. The ultimate underpinnings of the subject are shown to be the spectral theorem for unitary operators and Wold's theorem for isometric operators. Various generalizations are briefly indicated in a concluding section.
ISSN:0036-1445
1095-7200
DOI:10.1137/1021053