NDLI: Prime-length real-valued polynomial residue division algorithms

Content Provider	IEEE Xplore Digital Library
Author	Murakami, H.
Copyright Year	1991
Abstract	One class of efficient algorithms for computing a discrete Fourier transform (DFT) is based on a recursive polynomial factorization of the polynomial 1-z/sup -N/. The Bruun algorithm is a typical example of such algorithms. Previously, the Bruun algorithm, which is applicable only when system lengths are powers of two in its original form, is generalized and modified to be applicable to the case when the length is other than a power of two. This generalized algorithm consists of transforms T/sub d,f/ with prime d and real f in the range 0/spl les/f<0.5. T/sub d,0/ computes residues X(z)mod(1-z/sup -2/) and X(z)mod(1-2 cos(/spl pi/k/d)z/sup -1/+z/sup -2/), k=1, 2, ..., d-1, and T/sub d,f/ (f /spl ne/0) computes residues X(z)mod(1-2cos(2/spl pi/(f+k)/d)z/sup -1/+z/sup -2/), k=0, 1, ..., d-1 for a given real signal X(z) of length 2d. The purpose of this paper is to find efficient algorithms for T/sub d,f/. First, polynomial factorization algorithms are derived for T/sub d,0/ and T/sub d,1/4/. When f is neither 0 nor 1/4, it is not feasible to derive a polynomial factorization algorithm. Two different implementations of T/sub d,f/ for such f are derived. One implementation realizes T/sub d,f/ via a d-point DFT, for which a variety of fast algorithms exist. The other implementation realizes T/sub d,f/ via T/sub d, 1/4/, for which the polynomial factorization algorithm exists. Comparisons show that for d/spl ges/5, these implementations achieve better performance than computing each output of T/sub d,f/ separately.
Sponsorship	IEEE Signal Processing Society
Starting Page	2777
Ending Page	2788
Page Count	12
File Size	487494
File Format	PDF
ISSN	1053587X
Volume Number	50
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Signal processing algorithms Discrete Fourier transforms Convolution Sampling methods Prototypes Filters Discrete transforms Digital signal processing Fast Fourier transforms
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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