compendium

paper information and status

J. Kovačević and M. Püschel. Algebraic signal processing theory: Sampling for infinite and finite 1-D space. IEEE Trans. Signal Process., 58(1):242-257, Jan. 2010.


[ pdf | @ IEEE Xplore | bibtex]


abstract

We derive a signal processing framework, called space signal processing, that parallels time signal processing. As such, it comes in four versions (continuous/discrete, infinite/finite), each with its own notion of convolution and Fourier transform. As in time, these versions are connected by sampling theorems that we derive. In contrast to time, however, space signal processing is based on a different notion of shift, called space shift, which operates symmetrically. Our work rigorously connects known and novel concepts into a coherent framework; most importantly, it shows that the sixteen discrete cosine and sine transforms are the space equivalent of the discrete Fourier transform, and hence can be derived by sampling. The platform for our work is the algebraic signal processing theory, an axiomatic approach and generalization of linear signal processing that we recently introduced.


code

matlab

The zipped archive contains the readme file as well as the code to generate the results in the paper.

[download]


This work is licensed under a Creative Commons GNU General Public License. To view a copy of this license, visit http://creativecommons.org/licenses/GPL/2.0. If you use this code or any part thereof in your research or publication, please also include a reference to this paper. Thank you!


proofs

All necessary proofs are included in the paper.


contact

For more information or to report bugs contact jelenak at cmu dot edu.