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The duality property of the Discrete Fourier Transform based on Simpson's rule
Author(s) -
Singh P.,
Singh V.
Publication year - 2012
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.1604
Subject(s) - mathematics , duality (order theory) , discrete fourier transform (general) , multiplicative function , property (philosophy) , fourier transform , transformation (genetics) , dimension (graph theory) , matrix (chemical analysis) , transformation matrix , domain (mathematical analysis) , mathematical analysis , discrete frequency domain , pure mathematics , frequency domain , fourier analysis , fractional fourier transform , philosophy , biochemistry , chemistry , materials science , physics , kinematics , epistemology , classical mechanics , composite material , gene
The classical Discrete Fourier Transform (DFT) satisfies a duality property that transforms a discrete time signal to the frequency domain and back to the original domain. In doing so, the original signal is reversed to within a multiplicative factor, namely the dimension of the transformation matrix. In this paper, we prove that the DFT based on Simpson's method satisfies a similar property and illustrate its effect on a real discrete signal. The duality property is particularly useful in determining the components of the transformation matrix as well as components of its positive integral powers. Copyright © 2012 John Wiley & Sons, Ltd.