Warped discrete-Fourier transform: Theory and applications

Author

Makur, Anamitra ; Mitra, Sanjit K.

Author_Institution

Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India

Volume

48

Issue

9

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

1086

Lastpage

1093

Abstract

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

Keywords

FIR filters; all-pass filters; discrete Fourier transforms; matrix decomposition; signal reconstruction; spectral analysis; all-pass function; design method; finite sequence; frequency transformation; matrix factorization; perfect reconstruction filter bank; signal compression; spectral analysis; tunable FIR filter; warped discrete Fourier transform; z-transform; Discrete Fourier transforms; Discrete transforms; Filter bank; Finite impulse response filter; Frequency; Passband; Prototypes; Signal design; Signal resolution; Spectral analysis;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.948436

Filename

948436