Fast regular 2D algorithms for trigonometric transforms

Jaakko T. Astola; David Akopian

doi:10.1117/12.263300

10 January 1997 Fast regular 2D algorithms for trigonometric transforms

Jaakko T. Astola, David Akopian

Proceedings Volume 3024, Visual Communications and Image Processing '97; (1997) https://doi.org/10.1117/12.263300
Event: Electronic Imaging '97, 1997, San Jose, CA, United States

Abstract

2D fast cosine and sine transforms with regular structure are developed for 2ⁿ X 2ⁿ data points. These algorithms are extended versions of the 1D fast regular algorithms introduced in our recent paper. The rationale for these 2D algorithms for sine/cosine transforms in a 2D decomposition of data sequences into 2D subblocks with reduced dimension, rather than 1D, separable treatments for the columns and rows of the data sets. As a result the number of multiplications is 25 percent less than in row- column approach. Numerous algorithms of these type were proposed previously for discrete Fourier transform (DFT) and discrete cosine transform of type 2 (DCT-II). In DCT-II case the algorithms do not have a regular structure as is the case in DFT algorithms and motivation of this work is to derive 2D algorithms for discrete sine and cosine transforms with regular constant geometry structures. Extension to 2ⁿ X 2^m data points is straightforward.

Citation Download Citation

Jaakko T. Astola and David Akopian "Fast regular 2D algorithms for trigonometric transforms", Proc. SPIE 3024, Visual Communications and Image Processing '97, (10 January 1997); https://doi.org/10.1117/12.263300

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