Orthonormal FBs with rational sampling factors and oversampled DFT-modulated FBs

A connection and filter design

Ilker Bayram, Ivan Selesnick

Research output: Contribution to journalArticle

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

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Filter banks
Discrete Fourier transforms
Sampling
FIR filters
Parameterization

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

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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.",
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AU - Selesnick, Ivan

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