Frequency characterization of the discrete cosine transform

Hsieh-Sheng Hou; Daniel R. Tretter

doi:10.1117/12.23514

1 November 1990 Frequency characterization of the discrete cosine transform

Hsieh-Sheng Hou, Daniel R. Tretter

Proceedings Volume 1349, Applications of Digital Image Processing XIII; (1990) https://doi.org/10.1117/12.23514
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

Two types of frequency characterization of the discrete cosine transform (DCT) have been analyzed in detail. One is performed in the natural spatial frequency domain and the other in the eigenspace of the firstorder Markov stationary random process. In the past the direct conversion from Fourier transform toDCT has been very difficult. It requires either doubling of the input data or reshuf fling the input data sequency. In this paper we have derived a unitary transform that allows one to directly convert a Fourier transform of natural sequence input into a DCT. Furthermore though it is known that the DCT asymptotically approaches the KarhunenLoeve transform (KLT) of the firstorder Markov stationary random process no exact relationship between these two transforms has been given. This paper derives the exact relation and exhibits the frequency characteristics of a DCT. Applications to image data compression and enhancement are also included.

Citation Download Citation

Hsieh-Sheng Hou and Daniel R. Tretter "Frequency characterization of the discrete cosine transform", Proc. SPIE 1349, Applications of Digital Image Processing XIII, (1 November 1990); https://doi.org/10.1117/12.23514

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