Orthonormal FBs With Rational Sampling Factors and Oversampled DFT-Modulated FBs: A Connection and Filter Design

Bayram I., Selesnick I. W.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.57, no.7, pp.2515-2526, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 7
  • Publication Date: 2009
  • Doi Number: 10.1109/tsp.2009.2018356
  • Journal Name: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2515-2526
  • Istanbul Technical University Affiliated: No

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.