期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 56, 期 4, 页码 1502-1521出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2007.907919
关键词
Chinese remainder theorem; discrete Fourier transform (DFT); discrete cosine transform (DCT); discrete sine transform (DST); fast Fourier transform (FFT); polynomial algebra; representation theory
This paper presents a systematic methodology to derive and classify fast algorithms for linear transforms. The approach is based on the algebraic signal processing theory. This means that the algorithms are not derived by manipulating the entries of transform matrices, but by a stepwise decomposition or the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebraic principles that generalize the well-known Cooley-Tukey fast Fourier transform (FFT) and make the algorithms' derivations concise and transparent. Application to the 16 discrete cosine and sine transforms yields a large class of fast general radix algorithms, many of which have not been found before.
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