PROBABILITY ANALYSIS METHOD BY DISCRETE FAST FOURIER TRANSFORM

Fast Fourier Transform for Discrete Asian Options

This paper presents an efficient methodology for the discrete Asian options consistent with different types of underlying densities, especially non-normal returns as suggested by the empirical literature (Mandelbrot (1963) and Fama (1965)). The interest of this method is its flexibility compared to the more standard ones. Based on Fast Fourier Transform, the method is an enhanced version of the...

Octonion Discrete Fourier Transform : Fast Algorithms

 The color image from one of the color models, for instance the RGB model, can be transformed into the quaternion algebra and be represented as one quaternion image which allows to process simultaneously of all color components of the image. The color image can be also considered in different models with transformation to the octonion space with following processing in the 8-D frequency domain...

A New Fast Discrete Fourier Transform

This paper presents a new fast Discrete Fourier Transform (DFT) algorithm. By rewriting the DFT, a new algorithm is obtained that uses 2 n?2 (3n?13)+4n?2 real multiplications and 2 n?2 (7n? 29) + 6n + 2 real additions for a real data N = 2 n point DFT, comparable to the number of operations in the Split-Radix method, but with slightly fewer multiply and add operations in total. Because of the o...

Molecular Simulation with Discrete Fast Fourier Transform

Very fast discrete Fourier transform, using number theoretic transform

It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shif...