CA2086174A1 - Computational Structures for the Frequency-Domain Analysis of Signals and Systems - Google Patents

Computational Structures for the Frequency-Domain Analysis of Signals and Systems

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Publication number
CA2086174A1
CA2086174A1 CA2086174A CA2086174A CA2086174A1 CA 2086174 A1 CA2086174 A1 CA 2086174A1 CA 2086174 A CA2086174 A CA 2086174A CA 2086174 A CA2086174 A CA 2086174A CA 2086174 A1 CA2086174 A1 CA 2086174A1
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CA
Canada
Prior art keywords
structures
dft
cooley
tukey
radix
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Application number
CA2086174A
Other languages
French (fr)
Other versions
CA2086174C (en
Inventor
Duraisamy Sundararajan
M. Omair Ahmad
M. N. Srikanta Swamy
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Individual
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Individual
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Priority to CA002086174A priority Critical patent/CA2086174C/en
Priority to GB9322858A priority patent/GB2283592B/en
Publication of CA2086174A1 publication Critical patent/CA2086174A1/en
Application granted granted Critical
Publication of CA2086174C publication Critical patent/CA2086174C/en
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Discrete Mathematics (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)

Abstract

Since the invention of the radix-2 structure for the computation of the discrete Fourier transform (DFT) by Cooley and Tukey in 1965, the DFT has been widely used for the frequency-domain analysis and design of signals and systems in communications, digital signal processing, and in other areas of science and engineering. While the Cooley-Tukey structure is simpler, regular, and efficient, it has some drawbacks such as more complex multiplications than required by higher-radix structures, and the overhead operations of bit-reversal and data-swapping. The present invention provides a large family of radix-2 structures for the computation of the DFT of a discrete signal of N samples. A member of this set of structures is characterized by two parameters, u and v, where u (u = 2r, r =
1, 2, . . ., (log2 N)-1) specifies the size of each data vector applied at the two input nodes of a butterfly and v represents the number of consecutive stages of the structure whose multiplication operations are merged partially or fully. It is shown that the nature of the problem of computing the DFT is such that the sub-family of the structures with u = 2 suits best for achieving its solution. These structures have the features that eliminate or reduce the drawbacks of the Cooley-Tukey structure while retaining its simplicity and regularity.
A comprehensive description of the two most useful structures from this sub-family along with their hardware implementations is presented.
CA002086174A 1992-12-23 1992-12-23 Computational structures for the frequency-domain analysis of signals and systems Expired - Fee Related CA2086174C (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
CA002086174A CA2086174C (en) 1992-12-23 1992-12-23 Computational structures for the frequency-domain analysis of signals and systems
GB9322858A GB2283592B (en) 1992-12-23 1993-11-05 FFT butterfly arithmetic units

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CA002086174A CA2086174C (en) 1992-12-23 1992-12-23 Computational structures for the frequency-domain analysis of signals and systems
GB9322858A GB2283592B (en) 1992-12-23 1993-11-05 FFT butterfly arithmetic units

Publications (2)

Publication Number Publication Date
CA2086174A1 true CA2086174A1 (en) 1994-06-24
CA2086174C CA2086174C (en) 1998-08-25

Family

ID=25675776

Family Applications (1)

Application Number Title Priority Date Filing Date
CA002086174A Expired - Fee Related CA2086174C (en) 1992-12-23 1992-12-23 Computational structures for the frequency-domain analysis of signals and systems

Country Status (2)

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CA (1) CA2086174C (en)
GB (1) GB2283592B (en)

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3892956A (en) * 1971-12-27 1975-07-01 Bell Telephone Labor Inc Cascade digital fast fourier analyzer
FR2326743A1 (en) * 1975-10-02 1977-04-29 Thomson Csf DISCREET FOURIER TRANSFORMATION CALCULATOR
US4587626A (en) * 1981-10-13 1986-05-06 Trw Inc. Sum and difference conjugate discrete Fourier transform
US5303172A (en) * 1988-02-16 1994-04-12 Array Microsystems Pipelined combination and vector signal processor
US5093801A (en) * 1990-07-06 1992-03-03 Rockwell International Corporation Arrayable modular FFT processor

Also Published As

Publication number Publication date
GB9322858D0 (en) 1993-12-22
GB2283592A (en) 1995-05-10
CA2086174C (en) 1998-08-25
GB2283592B (en) 1998-10-14

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