Sampling theorem associated with the discrete cosine transform

Jelena Kovačević, Markus Püschel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

One way of deriving the discrete Fourier transform (DFT) is by equispaced sampling of periodic signals or signals on a circle. In this paper, we show that an analogous derivation can be used to obtain the DCT (type 2). To achieve this goal, we replace the circle by a line graph with symmetric boundary conditions, and define signal space, filter space, and filtering operation appropriately. Further, we derive the corresponding sampling theorem including the proper notions of "bandlimited" and "sinc function." The results show that, in a rigorous sense, the DCT is closely related to the DFT, and can be introduced without concepts from statistical signal processing as is the current practice.

Original languageEnglish (US)
Title of host publication2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
PagesIII357-III360
StatePublished - 2006
Event2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France
Duration: May 14 2006May 19 2006

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
ISSN (Print)1520-6149

Other

Other2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
CountryFrance
CityToulouse
Period5/14/065/19/06

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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  • Cite this

    Kovačević, J., & Püschel, M. (2006). Sampling theorem associated with the discrete cosine transform. In 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings (pp. III357-III360). [1660664] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 3).