Minimum multiplicative complexity algorithm for computing a single component of the discrete Fourier transform

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Abstract

A new algorithm for computing a single component of the discrete Fourier transform is presented. The algorithm, which is optimum in the sense that it requires the minimum number of multiplications, is based on the cyclotomic basis decomposition.

Section snippets

Gilson Jerônimo da Silva Jr. received the B.Sc. (with laurea), M.Sc. and Dr. degrees from the Federal University of Pernambuco (UFPE), Recife, Brazil, in 2006, 2008 and 2012, respectively, all in Electrical Engineering.

Dr. Jerônimo is currently an Adjunct Professor at the Electronics and Systems Department at UFPE. His research interests include digital signal and image processing, wavelets, filter banks, finite fields and fast algorithms for digital signal processing.

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Gilson Jerônimo da Silva Jr. received the B.Sc. (with laurea), M.Sc. and Dr. degrees from the Federal University of Pernambuco (UFPE), Recife, Brazil, in 2006, 2008 and 2012, respectively, all in Electrical Engineering.

Dr. Jerônimo is currently an Adjunct Professor at the Electronics and Systems Department at UFPE. His research interests include digital signal and image processing, wavelets, filter banks, finite fields and fast algorithms for digital signal processing.

Ricardo Menezes Campello de Souza was born in Recife. He received the B.Sc. and M.Sc. degrees from the Federal University of Pernambuco (UFPE), Recife, Brazil, in 1974 and 1979, respectively, and the PhD degree from the University of Manchester, England, in 1983, all in Electrical Engineering. Since 1978 he has been a member of staff at the Electronics and Systems Department, UFPE, where he is now an Associate Professor.

Dr. Campello de Souza is currently an Associate Editor of the Journal of Communication and Information Systems. His research interests include fast algorithms for digital signal processing, fractional and finite field transforms, cryptography, error-correcting codes and chess. He is a member of the Brazilian Society of Applied and Computational Mathematics and a senior member of the Brazilian Telecommunications Society.

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