E. Hitzer: Space-Time Fourier Transform, Convolution and Mustard Convolution


Eckhard Hitzer, Space-Time Fourier Transform, Convolution and Mustard Convolution, 15 Pages. Submitted to S. Bernstein and P. Cerejeiras (eds.), Complex Variables and Elliptic Equations (Taylor & Francis), Special Issue entitled “Clifford analysis – theory and applications”, 26 Jan. 2016. Preprint download: http://vixra.org/pdf/1601.0283v1.pdf

Abstract: In this paper we use the steerable space-time Fourier transform (SFT), and relate the classical convolution of the algebra for space-time $Cl(3,1)$-valued signals over the space-time vector space $\R^{3,1}$, with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the SFTs of the factor functions. In full generality do we express the classical convolution of space-time signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of space-time signals in terms of finite linear combinations of classical convolutions.

Keywords: Convolution, Mustard convolution, space-time Fourier transform, space-time signals, space-time domain, frequency domain

Source: http://vixra.org/abs/1601.0283

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