DocumentCode :
2745164
Title :
A new method mathematically links fast Fourier transform algorithms with fast cyclic convolution algorithms
Author :
Teixeira, Marvi ; Rodriguez, Domingo
Author_Institution :
Polytech. Univ. of Puerto Rico, Hato Rey, Puerto Rico
Volume :
2
fYear :
1994
fDate :
3-5 Aug 1994
Firstpage :
829
Abstract :
The cyclic convolution theorem is used to formally link certain factorizations of the DFT matrix to factorizations of the circulant matrices. As an example, the DFT matrix decomposition leading to the decimation in time fast Fourier transform is mathematically linked to a circulant matrix decomposition, which in turn leads to a fast cyclic convolution algorithm. Most importantly, permutations of the DFT matrix are shown to be related to permutations of the circulant matrices. It is therefore illustrated how certain factorizations, in one domain, could lead to fast algorithms in both domains, thus, providing further insight and needed unification
Keywords :
convolution; discrete Fourier transforms; fast Fourier transforms; matrix decomposition; DFT matrix; FFT algorithms; circulant matrices; cyclic convolution theorem; decimation in time FFT; factorizations; fast Fourier transform algorithms; fast algorithms; fast cyclic convolution algorithms; matrix decomposition; permutations; Convolution; Discrete Fourier transforms; Fast Fourier transforms; Frequency; Matrix decomposition; Microprocessors; Multidimensional systems; Very large scale integration; Writing;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Circuits and Systems, 1994., Proceedings of the 37th Midwest Symposium on
Conference_Location :
Lafayette, LA
Print_ISBN :
0-7803-2428-5
Type :
conf
DOI :
10.1109/MWSCAS.1994.518942
Filename :
518942
Link To Document :
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