Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: In this paper, a series inversion of the k-plane transform is presented, and estimates for the minimum number of discretely sampled direction sets at which the kplane transform must be known in order to recover a point function up to a given degree.
Abstract: The k-plane transform encompasses both the X-ray and Radon transforms. A series inversion which operates in the unified setting of the k-plane transform is presented. The author shows that with respect to either the Jacobi or the associated Laguerre polynomial bases for square integrable point functions, the k-plane transform assumes a block-diagonal-like form. Additionally, estimates are given for the minimum number of discretely sampled direction sets at which the k-plane transform must be known in order to recover a point function up to a given degree.
12 citations
TL;DR: It is shown that the short length DHTs used by the prime factor algorithm can be nested to lead to the Winograd Hartley transform algorithm.
Abstract: A prime factor algorithm for computing the discrete Hartley transform (DHT) is presented. It is shown that the short length DHTs used by the prime factor algorithm can be nested to lead to the Winograd Hartley transform algorithm.
12 citations
TL;DR: A discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations of multi-scale models, and the method is validated against finite element analysis.
Abstract: Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green’s function integrals are resolved, and the method is validated against finite element analysis.
12 citations
TL;DR: The improved Mellin transform is more accurate than the fast Fourier transform, converges faster to the Black- Scholes-Merton model, provides accurate comparable prices and the approach can be regarded as a good alternative to existing methods for the valuation of European call option on a dividend paying stock.
Abstract: This paper considers the valuation of European call options via the fast Fourier transform and the improved Mellin transform. The Fourier valuation techniques and Fourier inversion methods for density calculations add a versatile tool to the set of advanced techniques for pricing and management of financial derivatives. The Fast Fourier transform is a numerical approach for pricing options which utilizes the characteristic function of the underlying instrument’s price process. The Mellin transform has the ability to reduce complicated functions by realization of its many properties. Mellin’s transformation is closely related to an extended form of other popular transforms, particularly the Laplace transform and the Fourier transform. We consider the fast Fourier transform for the valuation of European call options. We also extend a framework based on the Mellin transforms and show how to modify the method to value European call options. We obtain a new integral equation to determine the price of European call by means of the improved Mellin transform. We show that our integral equation for the price of the European call option reduces to the Black-Scholes-Merton formula. The numerical results show that the tremendous speed of the fast Fourier transform allows option prices for a huge number of strikes to be evaluated very rapidly but the damping factor or the integrability parameter must be carefully chosen since it controls the intensity of the fluctuations and the magnitude of the functional values. The improved Mellin transform is more accurate than the fast Fourier transform, converges faster to the Black- Scholes-Merton model, provides accurate comparable prices and the approach can be regarded as a good alternative to existing methods for the valuation of European call option on a dividend paying stock.
12 citations