Haar filter banks for 1-D space signals

Aliaksei Sandryhaila, Jelena Kovačević, Markus Püschel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We derive the Haar filter bank for 1-D space signals, based on our recently introduced framework for 1-D space signal processing, termed this way since it is built on a symmetric space shift operation in contrast to the directed time shift operation. The framework includes the proper notions of signal and filter spaces, "z-transform," convolution, and Fourier transform, each of which is different from their time equivalents. In this paper, we extend this framework by deriving the proper notions of a Haar filter bank for space signal processing, and show that it has a similar yet different form compared to the time case. Our derivation also sheds light on the nature of filter banks and makes a case for viewing them as projections on subspaces rather than as based on filters.

Original languageEnglish (US)
Title of host publication2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Pages3505-3508
Number of pages4
DOIs
StatePublished - Sep 16 2008
Event2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP - Las Vegas, NV, United States
Duration: Mar 31 2008Apr 4 2008

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
CountryUnited States
CityLas Vegas, NV
Period3/31/084/4/08

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Keywords

  • Algebra
  • Fourier transforms
  • Haar transforms
  • Spectral analysis
  • Wavelet transforms

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Sandryhaila, A., Kovačević, J., & Püschel, M. (2008). Haar filter banks for 1-D space signals. In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP (pp. 3505-3508). [4518407] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2008.4518407