3 March 2000 Nonlinear Volterra-Weyl transforms
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It is well known that nonlinear time-invariant filtering may be viewed as a nonlinear superposition of time-shifted versions of the input signal, that is described as a time invariant Volterra convolution. Nonlinear superposition of time- and frequency shifted versions of the input signal is called Volterra-Weyl convolution. In the present paper, we associate with each orthogonal transform (Legandre, Hermite, Laguerre, Walsh, Haar, Gabor, fractional Fourier, wavelet, etc.) a family of generalized shift operators. Using them we construct a nonlinear superposition of generalized time-shifted versions of the input signal. We call such a superposition a generalized Volterra-Weyl convolution (VWC). Particular cases of the VWC are nonlinear Gabor and Zak transformations, generalized higher-order Wigner distribution and ambiguity functions.
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Ekaterina V. Labunets-Rundblad, Ekaterina V. Labunets-Rundblad, Laura Astola, Laura Astola, Valeri G. Labunets, Valeri G. Labunets, Jaakko T. Astola, Jaakko T. Astola, Karen O. Egiazarian, Karen O. Egiazarian, "Nonlinear Volterra-Weyl transforms", Proc. SPIE 3961, Nonlinear Image Processing XI, (3 March 2000); doi: 10.1117/12.379383; https://doi.org/10.1117/12.379383

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