Journal ArticleDOI
Mathematical foundations of signal processing
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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.Abstract:
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,...read more
Citations
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Spectral Analysis of Time Series.
TL;DR: In this article, the authors developed the theory behind Krishnaiah and Schuurmann's theoretical work reported in their report Approximations to the Distributions of the Traces of Complex Multivariate Beta and F Matrices.
Journal ArticleDOI
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Generalized FFTS - A Survey of Some Recent Results
TL;DR: This paper surveys some recent work directed towards generalizing the fast Fourier transform (FFT) from the point of view of group representation theory, and discusses generalizations of the FFT to arbitrary finite groups and compact Lie groups.
Book ChapterDOI
A First Survey of Gabor Multipliers
TL;DR: In this article, the authors describe various basic facts about Gabor multipliers and their continuous analogue, which they will call STFT-multipliers, obtained by going from the signal domain to some transform domain, and applying a pointwise multiplication operator before resynthesis.
Journal ArticleDOI
Analytical Fixed-Point Accuracy Evaluation in Linear Time-Invariant Systems
TL;DR: A new method based on an analytical approach is presented for the case of linear-time-invariant (LTI) systems that allows the automatic determination of the signal-to-quantization-noise-ratio (SQNR) expression at the system output according to the fixed-point data format.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
RANDOM DATA Analysis and Measurement Procedures
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.