Copyrights to these papers may be held by the publishers. The download files are preprints. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.
Aliaksei Sandryhaila, Jelena Kovacevic and Markus Püschel (Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 3505-3508, 2008)
Haar Filter Banks for 1-D Space Signals
Preprint (117 KB)
Published paper (link to publisher)
We recently introduced the framework for 1-D space signal processing, termed this way since it is built on a symmetric definition of the shift operation in contrast to the directed time shift operation. The framework includes the proper notion of signal and filter space, "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 composition of filters.Keywords: Algebraic signal processing theory: Current status, Filter banks