Fast and numerically stable algorithms for discrete cosine transforms
نویسندگان
چکیده
منابع مشابه
Fast and Numerically Stable Algorithms for Discrete Hartley Transforms and Applications to Preconditioning
The discrete Hartley transforms (DHT) of types I – IV and the related matrix algebras are discussed. We prove that any of these DHTs of length N = 2 can be factorized by means of a divide–and–conquer strategy into a product of sparse, orthogonal matrices where in this context sparse means at most two nonzero entries per row and column. The sparsity joint with orthogonality of the matrix factors...
متن کاملFast and stable algorithms for discrete spherical Fourier transforms
In this paper, we propose an algorithm for the stable and eecient computation of Fourier expansions of square integrable functions on the unit sphere S R 3 , as well as for the evaluation of these Fourier expansions at special knots. The heart of the algorithm is an eecient realization of discrete Legendre function transforms based on a modiied and stabilized version of the Driscoll{Healy algor...
متن کاملA Polynomial Approach to Fast Algorithms for Discrete Fourier-cosine and Fourier-sine Transforms
The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...
متن کاملBilinear algorithms for discrete cosine transforms of prime lengths
Abstract: 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 = 2q with m > 0 and q...
متن کاملDiscrete cosine and sine transforms - regular algorithms and pipeline architectures
In this paper, regular fast algorithms for discrete cosine transform (DCT) and discrete sine transform (DST) of types II–IV are proposed and mapped onto pipeline architectures. The algorithms are based on the factorization of transform matrices described earlier by Wang. The regular structures of the algorithms are advantageous when mapping them onto hardware although such algorithms do not rea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.07.015