Nonlinear signal solitaire

Ekaterina V. Labunets-Rundblad; Laura Astola; Valeri G. Labunets; Jaakko T. Astola; Karen O. Egiazarian

doi:10.1117/12.379384

3 March 2000 Nonlinear signal solitaire

Ekaterina V. Labunets-Rundblad, Laura Astola, Valeri G. Labunets, Jaakko T. Astola, Karen O. Egiazarian

Proceedings Volume 3961, Nonlinear Image Processing XI; (2000) https://doi.org/10.1117/12.379384
Event: Electronic Imaging, 2000, San Jose, CA, United States

Abstract

Integral transforms and the signal representations associated with them are important tools in applied mathematics and signal theory. The Fourier transform and the Laplace transform are certainly the best known and most commonly used integral transforms. However, the Fourier transform is just one of many ways of signal representation and there are many other transforms of interest. In the past 20 years, other analytical methods have been proposed and applied, for example, wavelet, Walsh, Legandre, Hermite, Gabor, fractional Fourier analysis, etc. Regardless of their particular merits they are not as useful as the classical Fourier representation that is closely connected to such powerful concepts of signal theory as linear and nonlinear convolutions, classical and high-order correlations, invariance with respect to shift, ambiguity and Wigner distributions, etc. To obtain the general properties and important tools of the classical Fourier transform for an arbitrary orthogonal transform we associate to it generalized shift operators and develop the theory of abstract harmonic analysis of signals and linear and nonlinear systems that are invariant with respect to these generalized shift operators.

Citation Download Citation

Ekaterina V. Labunets-Rundblad, Laura Astola, Valeri G. Labunets, Jaakko T. Astola, and Karen O. Egiazarian "Nonlinear signal solitaire", Proc. SPIE 3961, Nonlinear Image Processing XI, (3 March 2000); https://doi.org/10.1117/12.379384

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