The duality property of the Discrete Fourier Transform based on Simpson's rule | Zendy

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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.

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