Shift, scaling and derivative properties for the discrete cosine transform

Reeves, Robert W. & Kubik, Kurt (2006) Shift, scaling and derivative properties for the discrete cosine transform. Signal Processing, 86(7), pp. 1597-1603.

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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.

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5 citations in Scopus
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3 citations in Web of Science®

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ID Code: 10487
Item Type: Journal Article
Refereed: Yes
Keywords: DCT, Image compression, Derivative, Shift, Scale, Image matching, JPEG
DOI: 10.1016/j.sigpro.2005.09.041
ISSN: 0165-1684
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2006 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 30 Oct 2007 00:00
Last Modified: 29 Feb 2012 13:22

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