The nonuniform discrete Fourier transform and its applications in filter design. I. 1-D

Author

Bagchi, Sonali ; Mitra, Sanjit K.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

43

Issue

6

fYear

1996

fDate

6/1/1996 12:00:00 AM

Firstpage

422

Lastpage

433

Abstract

The nonuniform discrete Fourier transform (NDFT) of a sequence of length N is defined as samples of its z-transform evaluated at N distinct points located arbitrarily on the z-plane. The NDFT reduces to the conventional discrete Fourier transform (DFT) when these points are located on the unit circle at equally spaced angles. The flexibility offered by the NDFT in choosing the sampling points leads to a variable spectral resolution that can be controlled by the user. The NDFT is applied to nonuniform frequency sampling design of 1-D FIR filters. This method produces nearly optimal equiripple 1-D filters with greatly reduced design times as compared with the Parks-McClellan algorithm. Comparisons with filters designed by other methods are presented to demonstrate the effectiveness of the proposed method

Keywords

FIR filters; band-pass filters; discrete Fourier transforms; filtering theory; frequency response; low-pass filters; 1D FIR filters; design time reduction; filter design; nonuniform DFT; nonuniform frequency sampling design; optimal equiripple 1-D filters; variable spectral resolution; z-transform samples; Algorithm design and analysis; Chirp; Design methodology; Discrete Fourier transforms; Fast Fourier transforms; Finite impulse response filter; Frequency; Helium; Sampling methods; Signal processing algorithms;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.502315

Filename

502315