Generalised intermediate transforms: methods of computation and potential applications

  • Authors:

  • A. E. Mahdi

  • Affiliations:

  • Department of Electronic and Computer Engineering, University of Limerick, Limerick, Ireland

  • Venue:
  • Signal Processing
  • Year:
  • 2003

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Abstract

The Generalised Transform theory defines a class of orthogonal transforms that include the Fourier and Walsh transforms together with a set of transforms known as Intermediate Transforms. The latter are less familiar and are yet to receive serious attention regarding applicability and methods of computation. This paper attempts to address these two issues via the development of etticient methods for computation of the Intermediate Transforms suitable for both software and hardware implementation, and the identification of an application area for these transforms, Based on a radix-2 FFT algorithm, a novel and easy to implement genetic method for fast computation of any member of a given Generalised Transform set, has been developed. A potential area of application in real-time digital signal processing and communication systems has been identified, investigated and assessed quantitatively and qualitatively. This is based on employing the Intermediate Transforms as alternative tools to the discrete Fourier transform trading accuracy for speed. Computational speed advantages of the Intermediate Transforms over the FFT are demonstrated by a new high-speed, two-butterfly realisation method suitable for real-time, hardware processor-based implementation.