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Integer DCT-II by lifting steps. (English) Zbl 1036.65118
Haussmann, Werner (ed.) et al., Modern developments in multivariate approximation. Proceedings of the 5th international conference, Witten-Bommerholz, Germany, September 22–27, 2002. Basel: Birkhäuser (ISBN 3-7643-2195-4/hbk). ISNM, Int. Ser. Numer. Math. 145, 235-252 (2003).
Summary: In image compression, the discrete cosine transform of type II (DCT-II) is of special interest. In this paper we use a new approach to construct an integer DCT-II first considered by us [Reversible integer DCT algorithms. Preprint, Univ. Duisburg (2002)]. Our method is based on a factorization of the cosine matrix of type II into a product of sparse, orthogonal matrices. The construction of the integer DCT-II of length 8 works with lifting steps and rounding-off. We are expecially interested in the normwise error and the componentwise error when the integer DCT-II is compared with the exact DCT-II.
For the entire collection see [Zbl 1027.00021].

65T50 Numerical methods for discrete and fast Fourier transforms