DETECTION AND LOCALIZATIN OF POWER QUALITY DISTURBANSES BASED ON FAST FOURIER TRANSFORM AND DISCRETE FOURIER TRANSFORM

Wavelet transform based fast approximate Fourier transform

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coe cients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...

Finite Fourier Transform, Circulant Matrices, and the Fast Fourier Transform

Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...

Accuracy of the Discrete Fourier Transform and the Fast Fourier Transform

Fast Fourier transform (FFT)-based computations can be far more accurate than the slow transforms suggest. Discrete Fourier transforms computed through the FFT are far more accurate than slow transforms, and convolutions computed via FFT are far more accurate than the direct results. However, these results depend critically on the accuracy of the FFT software employed, which should generally be...

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...

Molecular Simulation with Discrete Fast Fourier Transform