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Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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TL;DR: In this article, a method for the practical computation of the exact discrete Fourier transforms (DFT), both the direct and the inverse ones, of a continuous function g given by its values gj at the points of a uniform grid FN generated by conjugacy classes of elements of finite adjoint order N in the fundamental region F of compact semisimple Lie groups.
Abstract: A versatile method is described for the practical computation of the exact discrete Fourier transforms (DFT), both the direct and the inverse ones, of a continuous function g given by its values gj at the points of a uniform grid FN generated by conjugacy classes of elements of finite adjoint order N in the fundamental region F of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when F is reduced to a one-dimensional segment, and for SU(2)×SU(2)×⋯×SU(2) in multidimensional cases. This simplest case turns out to be a version of the discrete cosine transform (DCT). Implementations, abbreviated as DGT for Discrete Group Transform, based on simple Lie groups of higher ranks, are to be considered separately. DCT is often taken to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of the two inverse discrete transforms are studied. The following properties of the continuous extension of DCT (called CEDCT) from the discrete tj∈FN to all t∈F are proven and exemplified. Like the standard DFT, the DCT also returns the exact values of {gj} on the N+1 points of the grid. However, unlike the continuous extension of the standard DFT: (a) The CEDCT function fN(t) closely approximates g(t) between the points of the grid as well; (b) for increasing N, the derivative of fN(t) converges to the derivative of g(t); (c) for CEDCT the principle of locality is valid. In this article we also use the continuous extension of the two-dimensional (2D) DCT, SU(2)×SU(2), to illustrate its potential for interpolation as well as for the data compression of 2D images.
29 citations
06 Apr 2003
TL;DR: A theorem is presented that decomposes a polynomial transform into smallerPolynomial transforms, and it is shown that the FFT is obtained as a special case, which is used to derive a new class of recursive algorithms for the discrete cosine transforms of type II and type III.
Abstract: The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFT of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (DCT) of type II and type III. In contrast to other approaches, we manipulate polynomial algebras instead of transform matrix entries, which makes the derivation transparent, concise, and gives insight into the algorithms' structure. The derived algorithms have a regular structure and, for 2-power size, minimal arithmetic cost (among known DCT algorithms).
29 citations
TL;DR: In this article, a 2-D systolic array algorithm for the discrete cosine transform (DCT) is presented, which is based on the inverse discrete Fourier transform (DFT) version of the Goertzel algorithm via Horner's rule.
Abstract: A 2-D systolic array algorithm for the discrete cosine transform (DCT) is presented. It is based on the inverse discrete Fourier transform (DFT) version of the Goertzel algorithm via Horner's rule. This array requires N cells and multipliers, takes square root N+2 clock cycles to produce a complete N-point DCT, and is able to process a continuous stream of data sequences. >
29 citations
25 May 2003
TL;DR: This work extends the Legendre transform as the slope transform to non-concave/non-convex functions and uses it to analyze a simple communication network and proposes an identification method for its transfer characteristic.
Abstract: We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data communication networks. We first extend the Legendre transform as the slope transform to non-concave/non-convex functions. We then use it to analyze a simple communication network. We also propose an identification method for its transfer characteristic, and we confirm the results using the ns-2 network simulator.
28 citations
TL;DR: A phase demodulation scheme using a discrete Hilbert transform that can change the interferometric phase by π/2 has been investigated in this article, where the phase distribution in the range of 15π (rad) can be demodulated with the proposed method.
Abstract: A phase demodulation scheme using a discrete Hilbert transform that can change the interferometric phase by π/2 has been investigated. In-quadrature components of a fringe pattern are obtained from one captured interferogram using a one-dimensional (1-D) discrete Hilbert transform and a 1-D discrete high-pass filtering that are based on a digital signal processing technique. The phase distribution in the range of 15π (rad) can be demodulated with the proposed method. The 1-D discrete Hilbert transform can be extended to two-dimensional calculation with a raster scanning procedure. © 2005 The Optical Society of Japan
28 citations