On a set of matrix algebras related to discrete Hartley-type transforms
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TLDR
In this article, a set of fast real transforms including the well known Hartley transform is fully investigated and the mixed radix splitting properties of Hartley-type transforms are examined in detail.Citations
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References
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Computational Frameworks for the Fast Fourier Transform
TL;DR: The Radix-2 Frameworks, a collection of general and high performance FFTs designed to solve the multi-Dimensional FFT problem of Prime Factor and Convolution, are presented.
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Conjugate Gradient Methods for Toeplitz Systems
Raymond H. Chan,Michael K. Ng +1 more
TL;DR: Some of the latest developments in using preconditioned conjugate gradient methods for solving Toeplitz systems are surveyed, finding that the complexity of solving a large class of $n-by-n$ ToePlitz systems is reduced to $O(n \log n)$ operations.
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The Discrete Cosine Transform
TL;DR: A direct proof of orthogonality, by calculating inner products, does not reveal how natural these cosine vectors are, so this work proves orthog onality in a different way.
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Fast algorithms for the discrete W transform and for the discrete Fourier transform
TL;DR: A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform as well as for the discrete Fourier transform, which makes new algorithms more efficient than conventional algorithms.
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