Lagrange M-th band filters and the construction of smooth M-band wavelets

Author

Heller, Peter Niels

Author_Institution

Aware Inc., Cambridge, MA, USA

fYear

1994

fDate

25-28 Oct 1994

Firstpage

108

Lastpage

111

Abstract

This paper develops a new explicit formula for the construction of M-th band maximally flat lowpass filters based on Lagrange interpolation. Both the minimum length and arbitrary length solutions are obtained. This leads to the construction of M-band wavelet filters with N vanishing wavelet moments as spectral factors of the new M-th band filters. One can then vary the free parameters of the general (non-minimal length) M-th band filter to obtain filters with better stopband attenuation than the minimal length filters, and wavelet bases with greater smoothness than the corresponding minimal length solutions. Remarkably, in the M-band case (M>2), one can simultaneously improve the stopband attenuation of the lowpass filters and obtain smoother wavelet bases

Keywords

interpolation; low-pass filters; smoothing methods; spectral analysis; wavelet transforms; Lagrange M-th band filters; Lagrange interpolation; maximally flat lowpass filters; minimal length filters; smooth M-band wavelets; spectral factors; stopband attenuation; Attenuation; Finite impulse response filter; Frequency domain analysis; Frequency response; Interpolation; Lagrangian functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP International Symposium on

Conference_Location

Philadelphia, PA

Print_ISBN

0-7803-2127-8

Type

conf

DOI

10.1109/TFSA.1994.467352

Filename

467352