Orthonormal FBs with rational sampling factors and oversampled DFT-modulated FBs: A connection and filter design

Ilker Bayram, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review

Abstract

Methods widely used to design filters for uniformly sampled filter banks (FBs) are not applicable for FBs with rational sampling factors and oversampled discrete Fourier transform (DFT)-modulated FBs. In this paper, we show that the filter design problem (with regularity factors/ vanishing moments) for these two types of FBs is the same. Following this, we propose two finite-impulse-response (FIR) filter design methods for these FBs. The first method describes a parameterization of FBs with a single regularity factor/vanishing moment. The second method, which can be used to design FBs with an arbitrary number of regularity factors/ vanishing moments, uses results from frame theory. We also describe how to modify this method so as to obtain linear phase filters. Finally, we discuss and provide a motivation for iterated DFT-modulated FBs.

Original languageEnglish (US)
Pages (from-to)2515-2526
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume57
Issue number7
DOIs
StatePublished - 2009

Keywords

  • DFT-modulated filter banks
  • Rational filter banks
  • Regularity factors
  • Vanishing moments

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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