TY - GEN
T1 - Haar filter banks for 1-D space signals
AU - Sandryhaila, Aliaksei
AU - Kovačević, Jelena
AU - Püschel, Markus
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Algebra
KW - Fourier transforms
KW - Haar transforms
KW - Spectral analysis
KW - Wavelet transforms
UR - http://www.scopus.com/inward/record.url?scp=51449095850&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=51449095850&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2008.4518407
DO - 10.1109/ICASSP.2008.4518407
M3 - Conference contribution
AN - SCOPUS:51449095850
SN - 1424414849
SN - 9781424414840
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3505
EP - 3508
BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
T2 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Y2 - 31 March 2008 through 4 April 2008
ER -