U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. of Rostock, 1999. Home/Search Document Not in Database Summary Related Articles Check |
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Invertible Integer DCT Algorithms - Plonka, Tasche (Correct)
....(2j 1) 2k 1) where n (0) 2=2 and n (j) 1 for j 2 f1; n 1g. In our notation a subscript of a matrix denotes the corresponding order, while a superscript gives the type of the matrix. Observe that these matrices are orthogonal (see e.g. 17] pp. 13 14, [18, 19]) The discrete cosine transforms of type II (DCT II) and of type IV (DCT IV) are linear mappings of R onto R , which are generated by C n , respectively. In [15] simple split radix algorithms are proposed for these transforms of radix 2 length n, which are based on factorizations of ....
U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. Rostock, 1999.
Split-Radix Algorithms for Discrete Trigonometric Transforms - Plonka, Tasche (Correct)
....complexity (see [9, 20, 21, 16] The best DCT algorithms require about 2 n log 2 n ops. A polynomial DCT algorithm generates a factorization (1.1) of C n with sparse, non orthogonal matrix factors M n , i.e. the factorization (1. 1) does not preserve the orthogonality of C n (see e.g. [19, 2, 23]) This fact leads to a bad numerical stability of these DCT algorithms [19, 2, 23] 3. Fast DCT algorithms via direct matrix factorization: Using simple properties of trigonometric functions one may nd direct factorizations of the transform matrix C n into a product of real, sparse matrices. ....
....log 2 n ops. A polynomial DCT algorithm generates a factorization (1.1) of C n with sparse, non orthogonal matrix factors M n , i.e. the factorization (1. 1) does not preserve the orthogonality of C n (see e.g. 19, 2, 23] This fact leads to a bad numerical stability of these DCT algorithms [19, 2, 23]. 3. Fast DCT algorithms via direct matrix factorization: Using simple properties of trigonometric functions one may nd direct factorizations of the transform matrix C n into a product of real, sparse matrices. The trigonometric approximation algorithm of Runge [18] can be considered as a rst ....
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U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. of Rostock, 1999.
Reversible integer DCT algorithms - Plonka, Tasche (Correct)
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U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. of Rostock, 1999.
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