Haar filter banks for 1-D space signals

Aliaksei Sandryhaila, Jelena Kovacevic, 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

Other

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

Fingerprint

Filter banks
filters
Signal processing
signal processing
Convolution
Fourier transforms
Mathematical transformations
shift
convolution integrals
derivation
projection

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

Cite this

Sandryhaila, A., Kovacevic, 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] https://doi.org/10.1109/ICASSP.2008.4518407

Haar filter banks for 1-D space signals. / Sandryhaila, Aliaksei; Kovacevic, Jelena; Püschel, Markus.

2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP. 2008. p. 3505-3508 4518407.

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

Sandryhaila, A, Kovacevic, J & Püschel, M 2008, Haar filter banks for 1-D space signals. in 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP., 4518407, pp. 3505-3508, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, Las Vegas, NV, United States, 3/31/08. https://doi.org/10.1109/ICASSP.2008.4518407
Sandryhaila A, Kovacevic J, Püschel M. Haar filter banks for 1-D space signals. In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP. 2008. p. 3505-3508. 4518407 https://doi.org/10.1109/ICASSP.2008.4518407
Sandryhaila, Aliaksei ; Kovacevic, Jelena ; Püschel, Markus. / Haar filter banks for 1-D space signals. 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP. 2008. pp. 3505-3508
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