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.

Algebraic signal processing theory: Current status, Filter banks