Paper Info
Title
Characterization of nonuniform perfect-reconstruction filterbanks using unit-step signal
Abstract
An algebraic characterization of nonuniform perfect reconstruction (PR) filterbanks with integer decimation factors is presented. The PR property is formulated in the z domain based on the response of the linear multirate systems to the delayed unit-step signals. This leads to a unique class of characterizing formulas that are necessary and sufficient conditions for the PR property and free from the complex roots of unity. Two related characterizations of nonuniform PR systems, in the form of necessary conditions, are also developed based on these formulas. As a concrete example, the results are then used to derive necessary and sufficient conditions for PR nonuniform delay chain filterbanks. The conditions show that nonuniform delay chain filterbanks are the signal processing realizations of the mathematical notion of the exact covering systems of congruence relations. Important results from the mathematics literature on the exact covering systems are introduced. The results elucidate the admissible factors of decimation for the nonuniform PR delay chain systems in settings with maximally distinct decimation factors. A simple test of the PR property for delay chain systems is also presented. The test is based on the divisibility of certain polynomials by the cyclotomic polynomials. Finally, multirate systems based on the Beatty sequences, which are the irrational generalization of the exact covering systems, are briefly discussed.
Year
DOI
Venue
2004
10.1109/TSP.2004.832011
IEEE Transactions on Signal Processing
Keywords
Field
DocType
eigensignal,linear multirate systems,nonuniform perfect-reconstruction,signal processing,integer decimation factor,perfect reconstruction,maximally distinct decimation factor,beatty sequences,pr property,perfect-reconstruction filterbank,integer decimation factors,nonuniform pr delay chain,disjoint covering systems,delay chain system,polynomial division,nonuniform delay chain filterbanks,sufficient condition,channel bank filters,nonuniform pr system,exactly covering sequences,filtering theory,exact covering systems,unit-step signal,pr delay chain systems,polynomials,cyclotomic polynomials,nonuniform perfect reconstruction,filter banks,pr nonuniform delay chain,cyclotomic polynomial,roots of unity,filter bank
Integer,Discrete mathematics,Signal processing,Applied mathematics,Algebraic number,Complex number,Decimation,Polynomial,Control theory,Cyclotomic polynomial,Filter bank,Mathematics
Journal
Volume
Issue
ISSN
52
9
1053-587X
Citations 
PageRank 
References 
2
0.62
7
Authors
3
Name
Order
Citations
PageRank
S. Samadi110612.83
M.O. Ahmad2723.17
M. N. Swamy310418.85