Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Face Recognition Using the Discrete Cosine Transform
International Journal of Computer Vision - Special issue: Research at McGill University
DCT algorithms for composite sequence lengths
IEEE Transactions on Signal Processing
New fast recursive algorithms for the computation of discretecosine and sine transforms
IEEE Transactions on Signal Processing
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This paper presents a strategy to design bilinear discrete cosine transform (DCT) algorithms of prime lengths. We show that by using multiplicative groups of integers, one can identify and arrange the computation as a pair of convolutions. When the DCT length p is such that (p - 1)/2 is odd, the computation uses two (p - 1)/2 point cyclic convolutions. When (p - 1)/2 = 2m q with m 0 and q odd, the computation requires one (p - 1)/2 point cyclic convolution and a combination of a q point cyclic convolution and a 2m point Hankel product. Using bilinear algorithms for convolutions and Hankel products, one gets a bilinear DCT algorithm. We also show that the additions required beyond the convolutions can be minimized by a small modification to the convolution algorithms. This minimization exploits the fact that efficient bilinear convolution algorithms are almost always based on Chinese Remainder Theorem.