Symmetric sine and cosine structures for trigonometric transforms

Yuk Hee Chan, Wan Chi Siu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this paper we firstly define two new formulations, the symmetric sine structure (SSS) and the symmetric cosine structure (SCS). Then we propose a simple algorithm to realize one-dimensional SCS and SSS with sequence lengths equal to 2m. We show that a 2m-length discrete Hartley transform can be realized through a 2m-1-length SCS and a 2m-1-length SSS, which achieves the same multiplicative complexity as the minimum number of multiplications reported in the literature. However, our approach gives the advantage of requiring less additions compared with conventional approaches. Furthermore, this approach can also be applied to realize a 2m-length real-valued discrete Fourier transform, which requires the lowest number of multiplications compared with conventional real-valued algorithms and needs no complex number operations as found in other real-valued algorithms.
Original languageEnglish
Pages (from-to)433-441
Number of pages9
JournalCircuits Systems and Signal Processing
Volume10
Issue number4
DOIs
Publication statusPublished - 1 Dec 1991

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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