Shift, scaling and derivative properties for the discrete cosine transform

Reeves, Robert and Kubik, Kurt (2006) Shift, scaling and derivative properties for the discrete cosine transform. Signal Processing, 86 7: 1597-1603. doi:10.1016/j.sigpro.2005.09.041

Author Reeves, Robert
Kubik, Kurt
Title Shift, scaling and derivative properties for the discrete cosine transform
Journal name Signal Processing   Check publisher's open access policy
ISSN 0165-1684
Publication date 2006
Sub-type Article (original research)
DOI 10.1016/j.sigpro.2005.09.041
Volume 86
Issue 7
Start page 1597
End page 1603
Total pages 7
Place of publication Amsterdam
Publisher Elsevier Science Bv
Collection year 2006
Language eng
Subject CX
Abstract A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.
Keyword DCT
image compression
image matching
Q-Index Code CX

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 09:13:30 EST