Moment-based fast discrete Hartley transform

  • Authors:

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

  • Affiliations:

  • Key Laboratory of State Education Ministry for Image Processing and Intelligent Control, Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technolog ...;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong;Department of Computer Science, University of Concordia, Montreal, Canada;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong

  • Venue:
  • Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
  • Year:
  • 2003

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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 ocr 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(N log2 N/log2 log2 N) and is superior to the O(N log2 N) in the classical FHT. The execution time of the systolic array is only O(N log2 N/log2 log2 N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.