Generalized transforms for DSP and generalized spectral analysis

  • Authors:
  • Michael J. Corinthios

  • Affiliations:
  • École Polytechnique de Montréal, C.P. 6079 Succ. Centre Ville, Montréal, Canada H3C3A7

  • Venue:
  • Systems Analysis Modelling Simulation - Special issue: Digital signal processing and control
  • Year:
  • 2003

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Abstract

Recent advances in computer, robotics and Internet technologies have enhanced the importance of digital signal processing tools, parallel processing and multi-processing research. The recent developments in microelectronics and fiber optics technologies have called for faster digital signal processors for data compression, coding, secure communication, and multimedia applications. Man-machine interaction, the adaptive control of fast moving objects, spaceships and increasingly intelligent and complex robotics have motivated research in faster computers and massively parallel processors. Adaptive on-line system identification of fast time varying systems is a problem that has received greater attention in recent years. Generalized spectral analysis transforms and factorizations thereof lead to highly efficient tools for parameter identification in the presence of noise and highly efficient coding techniques. This chapter presents novel spectral analysis definitions and general base parallel processors for the implementation of DSP algorithms, and modern generalized spectral analysis transforms destined for such high-speed applications. The Weighted Laplace and z-transform generalized spectra are shown to unmask the poles and zeros of finite duration continuous time and discrete time systems. The Generalized Chrestenson-Walsh transform is shown to be a generalization of the Fourier Transform and as such provides a wider range of coding and multimedia compression possibilities. Massive parallelism is implemented using general base hypercube transformations.