Journal ArticleDOI
A set of new fast algorithms for DCTs and DSTs
P. Siva Kumar,K.M.M. Prabhu +1 more
TLDR
These algorithms compute an N length DCT/DST using JV/4 and N/8 length DHTs in parallel, with some additional pre- and post-processing of the data, thereby ensuring numerical stability.Abstract:
A set of fast algorithms have been developed for discrete cosine transforms (DCT) and sine transforms (DST) using the discrete Hartley transform (DHT). These algorithms compute an N length DCT/DST using JV/4 and N/8 length DHTs in parallel, with some additional pre- and post-processing of the data. Also, they only use cosine and sine multipliers, thereby ensuring numerical stability.read more
Citations
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A fast Karhunen-Loeve transform for a class of random processes
TL;DR: The Karhunter-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this Karhunen- Loeve series expansion can be obtained via an FFT algorithm, which could be useful in data compression and other mean-square signal processing applications.
Book ChapterDOI
CHAPTER 1 – Discrete Cosine and Sine Transforms
TL;DR: The book presents the complete set of discrete cosine transforms and discrete sine transforms constituting the entire class of discrete sinusoidal unitary transforms, including their definitions, general mathematical properties, relations to the Karhunen-Loeve transform, with the emphasis on fast algorithms and integer approximations for their efficient implementations in the integer domain.
Journal ArticleDOI
Short communication: the fast DCT-IV/DST-IV computation via the MDCT
TL;DR: The careful analysis of regular structure of the new fast MDCT algorithm allows to extract a new DCT-IV/DST-IV computational structure and to suggest a new sparse matrix factorization of the D CT-IV matrix.
Journal ArticleDOI
Minimum bias spatial filters for beamspace direction-of-arrival estimation
Moeness G. Amin,Nitin Bhalla +1 more
TL;DR: The paper introduces the MB tapers for beamspace processing and compares their DOA estimation performance, using noise-subspace eignestructure methods, to that of the DPSS beams.
Journal ArticleDOI
On the computation of the length-2/sup m/ discrete cosine and sine transforms via the permuted difference coefficient
Ching-Huang Wei,Chang-Fuu Chen +1 more
TL;DR: An intrinsic property, wherein the set of numbers formed using the magnitudes of a basis vector's elements is the same for all basis vectors in a length-2/sup m/ type-III discrete sine transform and discrete cosine transform, is proved and it is shown that the roundoff error of the coefficients is less sensitive than that of the inputs.
References
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Journal ArticleDOI
Discrete Cosine Transform
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
Journal ArticleDOI
A new algorithm to compute the discrete cosine Transform
TL;DR: A new algorithm is introduced for the 2m-point discrete cosine transform that reduces the number of multiplications to about half of those required by the existing efficient algorithms, and it makes the system simpler.
Journal ArticleDOI
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.
Journal ArticleDOI
On computing the discrete Hartley transform
TL;DR: A complete set of fast algorithms for computing the discrete Hartley transform is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms.
Journal ArticleDOI
Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric data
TL;DR: This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one) and can easily be applied to real and real-symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.
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