Abstract
A new fast radix-p-algorithm (p ≧ 2) for the discrete cosine transform (DCT) and its inverse is presented. It is based on the divide-and-conquer method and on the arithmetic with Chebyshev polynomials. The algorithm can be applied for the efficient calculation of DCT's of arbitrary transform lengths and for the implementation of other discrete Vandermonde transforms withO(N logN) arithmetical operations.
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Higham, N. J.: Fast solution of Vandermonde-like systems involving orthogonal polynomials. IMA J. Numerical Anal.8, 473–486 (1988)
Golberg, M. A., Fromme, J. A.: On theL 2 convergence of collocation for the generalized airfoil equation. J. Math. Anal. Appl.71, 271–286 (1979)
Wagh, M. D., Ganesh, H.: A new algorithm for the discrete cosine transform of arbitrary number of points. IEEE Trans. Comput.29, 269–277 (1980)
Lee, B. G.: Input and output index mappings for the prime-factor-decomposed computation of discrete cosine transform. IEEE Trans. Acoust. Speech Signal Process.17, 237–244 (1989)
Makhoul, J.: A fast cosine transform in one and two dimensions. IEEE Trans. Acoust. Speech Signal Process.28(1), 27–34 (1980)
Steidl, G., Tasche, M.: Polynomial approach to fast algorithms for the discrete Fourier-cosine- and Fourier-sine-transforms. Math. Comp.56, 281–296 (1991)
Steidl, G., Tasche, M.: Fast algorithms for one- and two-dimensional discrete cosine transforms. In: Haussmann, W., Jetter, K. (eds.) Multivariate Approximation and Interpolation. ISNM Vol. 92. Basel: Birkhäuser 1989
Vetterli, M., Nussbaumer, H. J.: Simple FFT and DCT algorithms with reduced number of operations, Signal Process.6, 267–278 (1984)
Rao, K. R., Yip, P.: Discrete Cosine Transform. Boston, San Diego, New York, London, Sydney, Toronto: Academic Press 1990
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Steidl, G. Fast radix-p discrete cosine transform. AAECC 3, 39–46 (1992). https://doi.org/10.1007/BF01189022
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DOI: https://doi.org/10.1007/BF01189022