Moment-based fast discrete Hartley transform

J. G. Liu, F. H.Y. Chan, F. K. Lam, H. F. Li, George S.K. Fung

Research output: Contribution to journalArticlepeer-review

Abstract

A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying our earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(Nlog2N/log2log2N) and is superior to the O(Nlog2N) in the classical FHT. The execution time of the systolic array is only O(Nlog2N/log2log2N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.

Original languageEnglish (US)
Pages (from-to)1749-1757
Number of pages9
JournalSignal Processing
Volume83
Issue number8
DOIs
StatePublished - Aug 2003

Keywords

  • Discrete Hartley transform
  • Fast transform
  • Moment
  • Systolic array

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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