Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Pricing Bermudan Options in Lévy Process Models

Abstract: This paper presents a Hilbert transform method for pricing Bermudan options in Levy process models. The corresponding optimal stopping problem can be solved using a backward induction, where a sequence of inverse Fourier and Hilbert transforms need to be evaluated. Using results from a sinc expansion based approximation theory for analytic functions, the inverse Fourier and Hilbert transforms can be approximated using very simple rules. The approximation errors decay exponentially with the number of terms used to evaluate the transforms for many popular Levy process models. The resulting discrete approximations can be efficiently implemented using the fast Fourier transform. The early exercise boundary is obtained at the same time as the price. Accurate American option prices can be obtained by using Richardson extrapolation.

Hilbert Transform and Applications

Abstract: When x(t) is narrow-banded, |z(t)| can be regarded as a slow-varying envelope of x(t) while the phase derivative ∂t[tan −1(y/x)] is an instantaneous frequency. Thus, Hilbert transform can be interpreted as a way to represent a narrow-band signal in terms of amplitude and frequency modulation. The transform is therefore useful for diverse purposes such as latency analysis in neuro-physiological signals (Recio-Spinoso et al., 2011; van Drongelen, 2007), design of bizarre stimuli for psychoacoustic experiments (Smith et al., 2002), speech data compression for communication (Potamianos & Maragos, 1994), regularization of convergence problems in multi-channel acoustic echo cancellation (Liu & Smith, 2002), and signal processing for auditory prostheses (Nie et al., 2006).

A convolution approach to the circle Hough transform for arbitrary radius

Abstract: The Hough transform is a well-established family of algorithms for locating and describing geometric figures in an image. However, the computational complexity of the algorithm used to calculate the transform is high when used to target complex objects. As a result, the use of the Hough transform to find objects more complex than lines is uncommon in real-time applications. We describe a convolution method for calculating the Hough transform for finding circles of arbitrary radius. The algorithm operates by performing a three-dimensional convolution of the input image with an appropriate Hough kernel. The use of the fast Fourier transform to calculate the convolution results in a Hough transform algorithm with reduced computational complexity and thus increased speed. Edge detection and other convolution-based image processing operations can be incorporated as part of the transform, which removes the need to perform them with a separate pre-processing or post-processing step. As the Discrete Fourier Transform implements circular convolution rather than linear convolution, consideration must be given to padding the input image before forming the Hough transform.