Journal ArticleDOI
Fast decimation-in-time algorithms for a family of discrete sine and cosine transforms
Patrick C. Yip,K. R. Rao +1 more
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Fast decimation-in-time algorithms for the various discrete cosine transforms and discrete sine transforms are systematically developed, based on a radix-2 factorization of the transformation matrix, and indicate these to be attractive alternatives to existing algorithms in terms of computational complexity and structural simplicity.Abstract:
Fast decimation-in-time (DIT) algorithms for the various discrete cosine transforms (DCT) and discrete sine transforms (DST) are systematically developed, based on a radix-2 factorization of the transformation matrix. The results indicate these to be attractive alternatives to existing algorithms in terms of computational complexity and structural simplicity.read more
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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.
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.
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.
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.
Journal ArticleDOI
The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms
Markus Püschel,Jose M. F. Moura +1 more
TL;DR: This paper presents an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of Chebyshev polynomials.
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.
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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
Adaptive Coding of Monochrome and Color Images
Wen-Hsiung Chen,C. Smith +1 more
TL;DR: In this article, an efficient adaptive encoding technique using a new implementation of the Fast Discrete Cosine Transform (FDCT) for bandwidth compression of monochrome and color images is described.
Journal ArticleDOI
Adaptive transform coding of speech signals
R. Zelinski,P. Noll +1 more
TL;DR: The main result is that this adaptive transform coder performs better than all known nonpitch-tracking coding schemes; it extends the range of speech waveform coding to lower bit rates and closes the gap between vocoders and predictive waveform coders.