Journal ArticleDOI
On computing the discrete Fourier and cosine transforms
TLDR
An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transform.Abstract:
An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transformread more
Citations
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Journal ArticleDOI
The Design and Implementation of FFTW3
Matteo Frigo,Steven G. Johnson +1 more
TL;DR: It is shown that such an approach can yield an implementation of the discrete Fourier transform that is competitive with hand-optimized libraries, and the software structure that makes the current FFTW3 version flexible and adaptive is described.
Journal ArticleDOI
Lapped transforms for efficient transform/subband coding
TL;DR: Two lapped transforms for subband/transform coding of signals are introduced: a version of the lapped orthogonal transform (LOT), which can be efficiently computed for any transform length; and the modulated lapped transform (MLT), which is based on a modulated quadrature mirror (QMF) bank.
Journal ArticleDOI
Symmetric convolution and the discrete sine and cosine transforms
TL;DR: The author defines symmetric convolution, relates the DSTs and DCTs to symmetric-periodic sequences, and then uses these principles to develop simple but powerful convolution-multiplication properties for the entire family of DST sine and cosine transforms.
Journal ArticleDOI
Extended lapped transforms: properties, applications, and fast algorithms
TL;DR: In this article, the extended lapped transform (ELT) is introduced, as a generalization of the previously reported modulated Lapped Transform (MLT), which is a promising substitute for traditional block transforms in transform coding systems.
Journal ArticleDOI
Fast algorithm for computing discrete cosine transform
TL;DR: An efficient method for computing the discrete cosine transform (DCT) is proposed, which is a generalization of the radix 2 DCT algorithm, and the recursive properties of the DCT for an even length input sequence are derived.
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 Fast Computational Algorithm for the Discrete Cosine Transform
TL;DR: A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional DiscreteCosine Transform algorithms using the Fast Fourier Transform.
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
Comparative performance of various trigonometric unitary transforms for transform image coding
H. B. Kekre,J. K. Solanki +1 more
TL;DR: The performance of each of the unitary transforms in the trigonometric family is studied in terms of quantitative performance measures such as variance distribution, rate distortion, Wiener filtering and how well a transform decorrelates the data efficiently for possible bandwidth compression of a signal represented by a firstorder Markov process model.
Journal ArticleDOI
Reconsideration of "A Fast Computational Algorithm for the Discrete Cosine Transform"
TL;DR: Some corrections are made for the original paper "A fast computational algorithm for the discrete cosine transform," 1 which contains some errors of indexes and of multiplication factors.