General multifractional Fourier transform method based on the generalized permutation matrix group

General multifractional Fourier transform method based on the generalized permutation matrix group

The paper studies the possibility of giving a general multiplicity of the fractional Fourier transform (FRFT) with the intention of combining existing finite versions of the FRFT. We introduce a new class of FRFT that includes the conventional fractional Fourier transforms (CFRFTs) and the weighted-...

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Veröffentlicht in:IEEE transactions on signal processing 2005-01, Vol.53 (1), p.83-98
Hauptverfasser: Qiwen Ran, Yeung, D.S., Tsang, E.C.C., Qi Wang
Format: Artikel
Sprache:eng
Schlagworte:
Application software
Applied sciences
Computer simulation
Eigenvalues and eigenfunctions
Exact sciences and technology
Fourier transforms
Fractional Fourier transform
general multifractional Fourier transform
generalized permutation matrix group
Information, signal and communications theory
Kernel
Kernels
Mathematical analysis
Mathematical methods
Mathematical models
Optical filters
Optical signal processing
Permutations
Radio access networks
Recursion
Signal processing
Telecommunications and information theory
weighted fractional Fourier transform
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Zusammenfassung:The paper studies the possibility of giving a general multiplicity of the fractional Fourier transform (FRFT) with the intention of combining existing finite versions of the FRFT. We introduce a new class of FRFT that includes the conventional fractional Fourier transforms (CFRFTs) and the weighted-type fractional Fourier transforms (WFRFTs) as special cases. The class is structurally well organized because these new FRFTs, which are called general multifractional Fourier transform (GMFRFTs), are related with one another by the Generalized Permutation Matrix Group (GPMG), and their kernels are related with that of CFRFTs as the finite combination by the recursion of matrix. In addition, we have computer simulations of some GMFRFTs on a rectangular function as a simple application of GMFRFTs to signal processing.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2004.837397