Abstract
A method of synthesizing DCT fast algorithms for short lengths is proposed. The main ideas are data inclusion into a direct sum of real algebras and the transform interpretation in terms of multiplication rules in these algebras. The synthesized algorithms require less arithmetic operations than the known ones. Results of numerical experiments are given for images being coded with FAs of the DCT described in the present work
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Rao, K. R., Yip, P.: Discrete CosineTransform. Academic Press, San Diego, 1990.
Krupiczka, A.: Interblock Variance as a Segmentation Criterion in Image Coding. Mashine Graphics and Vision 5, Nos 1/2 (1996) 229–235
Chichyeva, M. A.: On a Specific of Biosignals Block Coding Based on Discrete Trigonometric Transforms. Proceedings of the 13th Biennial International Conference “Biosignal'96”, Czech republic, Brno (1996) 122–124
Hou, H. S.: A Fast Recursive Algorithm for Computing the Discrete Cosine Transform. IEEE Transactions on Acoustics, Speech and Signal Processing ASSP-35, No 10 (1987) 1455–1461
Suheiro, N., Hatori, M.: Fast Algorithms for the DFT and Other Sinusoidal Transforms. IEEE Transactions on Acoustics, Speech and Signal Processing ASSP-34, No 6 (1986) 642–644
Chan-Wan, Y.-H., Siu, C.: On the Realization of Discrete Cosine Transform Using the Distributed Arithmetic. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 39, No 9 (1992) 705–712
Heideman, M. T.: Computation of an Odd-Length DCT from a Real-Valued DFT of the Same Length. IEEE Trans. Signal Process 40, No 1 (1992) 54–61
Chernov, V. M.: Fast Algorithm of the Odd-Length Discrete Cosine Transform. Automatic Control and Computer Science 3 (1994) 62–70
Ireland, K., Rosen M.: A Classical Introduction to Modern Number Theory. Springer, 1982
Chernov, V. M.: Algorithms of Two-Dimensional Discrete Orthogonal Transforms Realized in the Hamilton-Eisenstein Codes. The Problem Transmission of Information 31, No 3 (1995) 38–46
Chichyeva, M. A.: Algorithms of Discrete Cosine Transforms with Data Representation in Eisenstein's Codes. Image Processing & Communications (to appear)
Wang, Z.: Fast algorithms for discrete W transform and for the discrete Fourier transform. IEEE Trans. Acoust., Speech, Signal Processing ASSP-32 (1984) 803–816
Chernov, V. M.: Arithmetic Methods in the Theory of Discrete Orthogonal Transforms. Proceedings SPIE 2363 (1995) 134–141
Chernov, V.M.: Fast Algorithms of Discrete Orthogonal Transforms for Data Represented in Cyclotomic Fields. Pattern Recogn. and Image Anal. 3, No 4 (1993) 455–458
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© 1997 Springer-Verlag Berlin Heidelberg
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Chernov, V.M., Chicheva, M.A. (1997). “One-step” short-length DCT algorithms with data representation in the direct sum of the associative algebras. In: Sommer, G., Daniilidis, K., Pauli, J. (eds) Computer Analysis of Images and Patterns. CAIP 1997. Lecture Notes in Computer Science, vol 1296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63460-6_167
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DOI: https://doi.org/10.1007/3-540-63460-6_167
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