Fourier Transform in the Application Science

Fourier Transform Application in the Computation of Lightning Electromagnetic Field

Atmospheric discharge is one of the most interesting and powerful natural phenomenon hiding from men its undiscovered features and secrets for centuries. Lightning discharges have been studied in many theoretical and experimental ways. However, application of Fourier transform has been introduced in this research only in recent few decades. It proved very useful in solving many lightning resear...

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...

Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm.

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

Application of the Fractional Fourier Transform to Moving Train Imaging

This paper introduces an imaging algorithm with application of fractional Fourier transform (FrFT) for ground moving train imaging by Ku-band ground-based radar. In view of the fact that the train speed is varying when acrossing the radar beam, the multiple Doppler parameters are estimated corresponding to different range positions, i.e., they are estimated from different sections of data in Fr...

Discrete integer Fourier transform in real space: elliptic Fourier transform