Project: Warped Discrete Fourier Transform

PEOPLE

Anamitra Makur, S.K.Mitra

OBJECTIVE

The discrete Fourier transform (DFT) is widely used in many applications.  The N-point DFT of a length-N sequence is given by the frequency samples of its z-trans­form evaluated at N equally spaced points on the unit circle.  For spectral analysis, the DFT provides a fixed fre­quency resolution.  In this project we have developed a new type of DFT, called the warped dis­crete Fourier transform (WDFT), which computes the frequency samples of the z-transform of a length-N se­quence at N non-uniformly spaced fre­quency points on the unit circle.  The non-uniformly spaced frequency points are defined by a speci­fied allpass warping function.  An exact computation scheme has been developed requir­ing much less computation than the direct computation of the WDFT. Applications of the WDFT considered in this project are spectral analysis of two closely spaced sinusoids, design of non-uniform perfect reconstruc­tion QMF banks using warped DFT and subband coding, and design of tunable FIR filters.  A paper containing the results of this project has been presented at a conference [2].  An expanded version of this work will appear in a journal [1].

PUBLICATIONS

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1. A. Makur and S. K. Mitra, "Warped discrete Fourier transform: Theory and applications," IEEE Trans. on Circuits & Systems, Part I, 2001 - to be published.

2. S. K. Mitra and A. Makur, "Warped discrete Fourier transform," Proc. IEEE Workshop on Digital Signal Processing, Bryce, UT, August 1998.