Topic
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.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, it was shown that the Fourier transform is not contained in a finite union of arithmetic progressions, but instead can be constructed by applying the Poisson Summation Formula finitely many times.
Abstract: We give a simple proof of the fact, first proved in a stronger form in Lev and Olevskii (Quasicrystals with discrete support and spectrum, arXiv preprint arXiv:1501.00085
, 2014), that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson Summation Formula finitely many times. More specifically the support of both the measure and its Fourier Transform are not contained in a finite union of arithmetic progressions.
18 citations
TL;DR: It is shown how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform.
Abstract: We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (Math Finance 18(3):337–384, 2008) and Fusai et al. (Eur J Oper Res 251(4):124–134, 2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Levy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering.
18 citations
TL;DR: The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT.
Abstract: This paper presents a novel approach to the Fourier analysis of multichannel time series. Orthogonal matrix functions are introduced and are used in the definition of multichannel Fourier series of continuous-time periodic multichannel functions. Orthogonal transforms are proposed for discrete-time multichannel signals as well. It is proven that the orthogonal matrix functions are related to unitary transforms (e.g., discrete Hartley transform (DHT), Walsh-Hadamard transform), which are used for single-channel signal transformations. The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT. Therefore, fast algorithms for their computation can be easily constructed. Simulations on the use of discrete multichannel transforms on color image compression have also been performed.
17 citations
12 Dec 2007
TL;DR: A real-time block-based gradient domain HDR compression for image or video applications and solves the Poisson equation on the attenuated gradient field block by block to reconstruct a low dynamic range image.
Abstract: Due to progress in high dynamic range (HDR) capture technologies, the HDR image or video display on conventional LCD devices has become an important topic. Many tone mapping algorithms are proposed for rendering HDR images on conventional displays, but intensive computation time makes them impractical for video applications. In this paper, we present a real-time block-based gradient domain HDR compression for image or video applications. The gradient domain HDR compression is selected as our tone mapping scheme for its ability to compress and preserve details. We divide one HDR image/frame into several equal blocks and process each by the modified gradient domain HDR compression. The gradients of smaller magnitudes are attenuated less in each block to maintain local contrast and thus expose details. By solving the Poisson equation on the attenuated gradient field block by block, we are able to reconstruct a low dynamic range image. A real-time Discrete Sine Transform (DST) architecture is proposed and developed to solve the Poisson equation. Our synthesis results show that our DST Poisson solver can run at 50 MHz clock and consume area of 9 mm2 under TSMC 0.18 um technology.
17 citations