A Unified Approach to Fast Algorithms of Discrete Trigonometric Transforms

Abstract

We present a unified approach to fast algorithms of various discrete trigonometric transforms. With the help of so-called Euler formulas we describe an elegant and useful connection between Fourier matrices and trigonometric matrices. It is known that FFTs are closely related to the factorizations of the unitary Fourier matrix into a product of unitary sparse matrices. Using these Euler formulas and FFTs, we obtain fast algorithms of discrete trigonometric transforms. As a further consequence of these Euler formulas and Gaussian sums we compute all eigenvalues of some trigonometric matrices.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013761

Entities

People

  • Hansmartin Zeuner
  • Manfred Tasche

Organizations

  • University of Rostock

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Algorithms
  • Chebyshev Polynomials
  • Computations
  • Eigenvalues
  • Electrical Engineering
  • Equations
  • Fast Fourier Transforms
  • Identities
  • Image Compression
  • Mathematical Analysis
  • Mathematics
  • Orthogonality
  • Polynomials
  • Signal Processing
  • Technical Information Centers
  • Universities

Fields of Study

  • Engineering

Readers

  • Inertial Navigation Systems.
  • Linear Algebra