Algebraic signal processing theory: Sampling for infinite and finite 1-D space

Jelena Kovacevic, Markus Püschel

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number5204282
Pages (from-to)242-257
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume58
Issue number1
DOIs
StatePublished - Jan 1 2010

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Signal processing
Sampling
Convolution
Discrete Fourier transforms
Fourier transforms

Keywords

  • Algebra
  • Convolution
  • Discrete cosine and sine transforms
  • Fourier cosine transform
  • Module
  • Signal model
  • Space shift

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Algebraic signal processing theory : Sampling for infinite and finite 1-D space. / Kovacevic, Jelena; Püschel, Markus.

In: IEEE Transactions on Signal Processing, Vol. 58, No. 1, 5204282, 01.01.2010, p. 242-257.

Research output: Contribution to journalArticle

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