Methods for designing efficient parallel-recursive filter structures for computing discrete transforms

Analytical and numerical approaches are presented for the design of first-order and second-order recursive digital filter banks for computing linear, discrete transforms. This subject has been studied extensively for the case of trigonometric transforms. The focus of this paper is on discrete polyno...

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Bibliographic Details
Published in:Telecommunication systems 2000-01, Vol.13 (1), p.69
Main Authors: Kozick, Richard J, Aburdene, Maurice F
Format: Article
Language:English
Subjects:
Algorithms
Design
Efficiency
Field programmable gate arrays
Fourier transforms
Polynomials
Studies
Systems analysis
Telecommunications systems
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Summary:Analytical and numerical approaches are presented for the design of first-order and second-order recursive digital filter banks for computing linear, discrete transforms. This subject has been studied extensively for the case of trigonometric transforms. The focus of this paper is on discrete polynomial transforms, and Clenshaw's recurrence formulae are used to design the second-order filters. The efficiency of the implementation for a specific transform is dependent upon the characteristics of recurrence relations for the transform basis vectors. Efficient implementations are derived for the discrete cosine transform and the inverse discrete Legendre transform from analytical expressions for basis vector recurrence relations. A numerical procedure is presented to search for the existence and parameters of an efficient implementation when analytical expressions for the basis vector recurrence relations are unknown. [PUBLICATION ABSTRACT]
ISSN:1018-4864
1572-9451
DOI:10.1023/A:1019175519056