Interesting properties of the discrete cosine transform

Authors:
H. S. Hou;D. R. Tretter;M. J. Vogel
Affiliations:
Electronics and Sensors Division, Engineering Group, The Aerospace Corporation, 2350 East El Segundo Boulevard, El Segundo, California, 90245, USA;Electronics and Sensors Division, Engineering Group, The Aerospace Corporation, 2350 East El Segundo Boulevard, El Segundo, California, 90245, USA;Electronics and Sensors Division, Engineering Group, The Aerospace Corporation, 2350 East El Segundo Boulevard, El Segundo, California, 90245, USA
Venue:
Journal of Visual Communication and Image Representation
Year:
1992

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Abstract

Among the various image data compression methods, the discrete cosine transform (DCT) has emerged as a popular method in gray-scale image compression. This paper presents detailed analyses of several interesting properties of the DCT, which can be described in three parts: the frequency characteristics, the filtering properties, and the subband properties. These analyses provide insights into the following topics: (1) the frequency distribution of the DCT in terms of the Fourier transform components, (2) the filtering characteristics of the DCT, and (3) the use of the DCT as subband filters. Surprisingly, based on our analyses, the DCT behaves very much like subband filters, with potential applications not only to image data compression but also to image analysis. The formulas presented in this paper have been checked for correctness by computer simulations, and applications to image data compression have been demonstrated with simulation results.