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

Jelena Kovačević, Markus Püschel

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Jan 2010


  • 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


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