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Warped Discrete-Fourier Transform:Theory and Applications

Makur, Anamitra and Mitra, Sanjit K (2001) Warped Discrete-Fourier Transform:Theory and Applications. In: IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48 (9). pp. 1086-1093.


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In this paper, we advance the concept of warped discrete- Fourier transform (WDFT), which is the evaluation of frequency samples of the z-transform of a finite-length sequence at nonuniformly spaced points on the unit circle obtained by a frequency transformation using an allpass warping function. By factorizing the WDFT matrix, we propose an exact computation scheme for finite sequences using less number of operations than a direct computation. We discuss various properties of WDFT and the structure of the factoring matrices. Examples of WDFT for first- and second-order allpass functions is also presented. Applications of WDFT included are spectral analysis, design of tunable FIR filters, and design of perfect reconstruction filterbanks with nonuniformly spaced passbands of filters in the bank. WDFT is efficient to resolve closely spaced sinusoids. Tunable FIR filters may be designed from FIR prototypes using WDFT. In yet another application, warped PR filterbanks are designed using WDFT and are applied for signal compression.

Item Type: Journal Article
Publication: IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications
Publisher: IEEE
Additional Information: 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Allpass;DFT;frequency warping;warped DFT
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 22 Aug 2008
Last Modified: 19 Sep 2010 04:16
URI: http://eprints.iisc.ac.in/id/eprint/1965

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