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 (IEEE Transactions on Signal Processing, Vol. 60, No. 5, pp. 2247-2259, 2012)
Algebraic Signal Processing Theory: 1-D Nearest-Neighbor Models
Preprint (241 KB)
Published paper (link to publisher)
Bibtex

We present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials. We demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest-neighbor shift introduced in this paper. Using the algebraic signal processing theory, we construct signal models based on this shift and derive their corresponding signal processing concepts, including the proper notions of signal and filter spaces, z-transform, convolution, spectrum, and Fourier transform. The presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials.

Keywords:
Signal transforms, Algebraic signal processing theory: Current status, Orthogonal polynomials, Alternative signal models