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Special relativistic Fourier transformation and convolutions
Author(s) -
Hitzer Eckhard
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5502
Subject(s) - convolution (computer science) , mathematics , overlap–add method , convolution theorem , fourier transform , circular convolution , convolution power , mathematical analysis , vector space , transformation (genetics) , discrete time fourier transform , space (punctuation) , pure mathematics , fourier analysis , fractional fourier transform , computer science , biochemistry , chemistry , machine learning , artificial neural network , operating system , gene
In this paper, we use the steerable special relativistic (space‐time) Fourier transform (SFT) and relate the classical convolution of the algebra for space‐time C l (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.