Commutativity of block decimators and expanders with arbitrary rational sampling ratios and block lengths

https://doi.org/10.1016/j.dsp.2012.03.002Get rights and content

Abstract

It is well known that samplers are linear time varying systems, so in general, the commutativity of samplers does not hold. There are some existing results on the commutativity of conventional decimators and expanders, block samplers with the same integer block lengths but different integer sampling ratios, and block samplers with different integer block lengths and integer sampling ratios. This paper extends the existing results to a necessary and sufficient condition for the commutativity of block decimators and expanders with arbitrary rational sampling ratios and block lengths.

Section snippets

Bingo Wing-Kuen Ling received the B.Eng. (Hons) and M.Phil. degrees from the department of Electronic and Computer Engineering, the Hong Kong University of Science and Technology, in 1997 and 2000, respectively, and the Ph.D. degree in the department of Electronic and Information Engineering from the Hong Kong Polytechnic University in 2003. In 2004, he joined the Kingʼs College London as a Lecturer. He serves as the technical committee of the nonlinear circuits and systems group of the IEEE

References (11)

  • Xiang-Gen Xia et al.

    Multirate filter banks with block sampling

    IEEE Trans. Signal Process.

    (1996)
  • Masoud R.K. Khansari et al.

    Subband decomposition of signals with generalized sampling

    IEEE Trans. Signal Process.

    (1993)
  • Kambiz Nayebi, Thomas P. Barnwell III, Mark J.T. Smith, Block decimated analysis–synthesis filter banks, in:...
  • Charlotte Yuk-Fan Ho et al.

    Representations of linear dual rate system via single SISO LTI filter, conventional sampler and block sampler

    IEEE Trans. Circuits Syst. II Trans. Briefs

    (2008)
  • Lili Liang et al.

    Nonuniform directional filter banks with arbitrary frequency partitioning

    IEEE Trans. Image Process.

    (2011)
There are more references available in the full text version of this article.

Cited by (3)

Bingo Wing-Kuen Ling received the B.Eng. (Hons) and M.Phil. degrees from the department of Electronic and Computer Engineering, the Hong Kong University of Science and Technology, in 1997 and 2000, respectively, and the Ph.D. degree in the department of Electronic and Information Engineering from the Hong Kong Polytechnic University in 2003. In 2004, he joined the Kingʼs College London as a Lecturer. He serves as the technical committee of the nonlinear circuits and systems group of the IEEE Circuits and Systems Community, and was awarded the best reviewer prize from the IEEE Instrumentation and Measurement Society. He has also served as the guest editor-in-chief of several special issues of highly rated international journals, such as the Circuits, Systems and Signal Processing, and the American Journal of Engineering and Applied Sciences, and is currently an associate editor of the International Journal of Bifurcation and Chaos, and the Circuits, Systems and Signal Processing. He has published an undergraduate textbook, a research monograph, several book chapters, 60 internationally leading journal and more than fifty highly rated international conference papers. He has held six visiting positions and delivered ∼20 seminars in the field of image processing, time frequency analysis, optimization theory, symbolic dynamics as well as fuzzy and impulsive control theory.

Charlotte Yuk-Fan Ho received the B.Eng. (Hons) degree from the department of Electronic and Computer Engineering, the Hong Kong University of Science and Technology in 2000, and the M.Phil. Degree from the Department of Electronic and Information Engineering, the Hong Kong Polytechnic University, in 2003. She is pursuing her Ph.D. study at the Queen Mary, University of London. Her research interests include image processing, filter banks and wavelets theory, functional inequality constrained optimization problems, symbolic dynamics as well as fuzzy and impulsive control theory.

Zoran Cvetković received the Dipl.Ing.El. and Mag. El. degrees from the School of Electrical Engineering, University of Belgrade, Yugoslavia, in 1989 and 1992, respectively, the M.Phil. from Columbia University in 1993, and the Ph.D. in electrical engineering from the University of California, Berkeley, in 1995. He joined Kingʼs College London as a Reader in Signal Processing in 2004. Before that he was with the Division of Engineering and Applied Sciences of Harvard University, and in the period from 1997 to 2002, with the Center for Information Sciences Research of AT&T Shannon Laboratory. He was also involved in the research activities of Keck Center for Integrative Neuroscience, University of California, San Francisco, and the Signal Processing Laboratory at EPF Lausanne, Switzerland, and the research and teaching at the University of Belgrade. He is a Senior Member of the IEEE and an Associate Editor for IEEE Transactions on Signal Processing.

1

Fax: +44 (0)20 7882 7997.

2

Fax: +44 (0)20 7848 2932.

View full text