Numerical computation of the fourier transform using Laguerre functions and the Fast Fourier Transform

1980 ◽  
Vol 36 (2) ◽  
pp. 197-209 ◽  
Author(s):  
H. Weber
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Numerical Computation ◽  
Laguerre Functions ◽  
The Fourier Transform

Fast Fourier Transform – Calculation and Interpretation

2008 ◽  
Vol 3 (4) ◽  
pp. 74-86
Author(s):  
Boris A. Knyazev ◽  
Valeriy S. Cherkasskij
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Signal Theory ◽  
Correct Interpretation ◽  
The Fourier Transform ◽  
Application Programs ◽  
Physics Problems

The article is intended to the students, who make their first steps in the application of the Fourier transform to physics problems. We examine several elementary examples from the signal theory and classic optics to show relation between continuous and discrete Fourier transform. Recipes for correct interpretation of the results of FDFT (Fast Discrete Fourier Transform) obtained with the commonly used application programs (Matlab, Mathcad, Mathematica) are given.

Elimination of minimal FFT grid-size limitations

2002 ◽  
Vol 35 (4) ◽  
pp. 505-505 ◽  
Author(s):  
David A. Langs
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Input Data ◽  
Complex Structure ◽  
Grid Size ◽  
Structure Factors ◽  
The Fourier Transform

The fast Fourier transform (FFT) algorithm as normally formulated allows one to compute the Fourier transform of up toNcomplex structure factors,F(h),N/2 ≥h> −N/2, if the transform ρ(r) is computed on anN-point grid. Most crystallographic FFT programs test the ranges of the Miller indices of the input data to ensure that the total number of grid divisions in thex,yandzdirections of the cell is sufficiently large enough to perform the FFT. This note calls attention to a simple remedy whereby an FFT can be used to compute the transform on as coarse a grid as one desires without loss of precision.

scholarly journals Implementation of FFT Architecture using Various Adders

2019 ◽  
Vol 8 (10) ◽  
pp. 3750-3755
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Orthogonal Frequency Division Multiplex ◽  
Cell Phones ◽  
Frequency Division ◽  
Ripple Carry Adder ◽  
Significant Area ◽  
Area Optimization ◽  
The Fourier Transform

In 1965 a technique called Fast Fourier Transform (FFT) was invented to find the Fourier Transform. This paper compares three architectures, the basic architecture/ non-reduced architecture of FFT, decomposed FFT architecture without retiming and decomposed FFT architecture with retiming. In each case, the adder used will be Ripple Carry Adder (RCA) and Carry Save Adder (CSA). A fast Fourier transform (FFT) calculates the discrete Fourier transform (DFT) or the inverse (IDFT) of a sequence. Fourier analysis transforms a signal from time to frequency domain or vice versa. One of the most burgeoning use of FFT is in Orthogonal Frequency Division Multiplex (OFDM) used by most cell phones, followed by the use in image processing. The synthesis has been carried out on Xilinx ISE Design Suite 14.7. There is a decrease in delay of 0.824% in Ripple Carry Adder and 6.869% in Carry Save Adder, further the reduced architecture for both the RCA and CSA architectures shows significant area optimization (approximately 20%) from the non-reduced counterparts of the FFT implementation.

Computing the Fourier transform in geophysics with the transform decomposition DFT

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1707-1709
Author(s):  
Michael J. Reed ◽  
Hung V. Nguyen ◽  
Ronald E. Chambers
Keyword(s):  
Fourier Transform ◽  
Phase Shift ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Large Percentage ◽  
Computationally Efficient ◽  
Operation Count ◽  
The Fourier Transform

The Fourier transform and its computationally efficient discrete implementation, the fast Fourier transform (FFT), are omnipresent in geophysical processing. While a general implementation of the discrete Fourier transform (DFT) will take on the order [Formula: see text] operations to compute the transform of an N point sequence, the FFT algorithm accomplishes the DFT with an operation count proportional to [Formula: see text] When a large percentage of the output coefficients of the transform are not desired, or a majority of the inputs to the transform are zero, it is possible to further reduce the computation required to perform the DFT. Here, we review one possible approach to accomplishing this reduction and indicate its application to phase‐shift migration.

A note on 2-D Hartley transform

Geophysics ◽  
1994 ◽  
Vol 59 (7) ◽  
pp. 1150-1155 ◽  
Author(s):  
N. L. Mohan ◽  
L. Anand Babu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Seismic Signal ◽  
Clear Definition ◽  
Hartley Transform ◽  
The Fourier Transform ◽  
Definition Of ◽  
Seismic Signal Processing

In recent years the application of the Hartley transform, originally introduced by Hartley (1942), has gained importance in seismic signal processing and interpretation (Saatcilar et al., 1990, 1992). The Hartley transform is similar to the Fourier transform but is computationally much faster than even the fast Fourier transform (Bracewell, 1983; Bracewell et al., 1986; Sorensen et al., 1985; Pei and Wu, 1985; Duhamel and Vetterli, 1987; Zhou, 1992). Surprisingly, we have not seen a clear definition of the 2-D Hartley transform in the published literature.

scholarly journals FFT based convolution

2010 ◽  
Author(s):  
Gaetan Lehmann
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Performance Comparison ◽  
Convolution Filter ◽  
The Fourier Transform ◽  
Large Kernel ◽  
A Performance

The Fourier transform of the convolution of two images is equal to the product of their Fourier transform. With this definition, it is possible to create a convolution filter based on the Fast Fourier Transform (FFT). The interesting complexity characteristics of this transform gives a very efficient convolution filter for large kernel images.This paper provides such a filter, as well as a detailed description of the implementation choices and a performance comparison with the “simple” itk::ConvolutionImageFilter.

scholarly journals On the Numerical Computation of the Mittag–Leffler Function

2019 ◽  
Vol 20 (6) ◽  
pp. 725-736 ◽  
Author(s):  
Manuel D. Ortigueira ◽  
António M. Lopes ◽  
José Tenreiro Machado
Keyword(s):  
Fourier Transform ◽  
Fractional Calculus ◽  
Laplace Transform ◽  
Fast Fourier Transform ◽  
Numerical Computation ◽  
Fractional Order ◽  
Power Law ◽  
Computational Time ◽  
Integral Formulas

AbstractThe Mittag–Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.

Research of a New Power Quality Detection System Based on ARM

2014 ◽  
Vol 568-570 ◽  
pp. 1825-1833
Author(s):  
Yan Qing Peng ◽  
Feng Wang ◽  
Ji Zhang ◽  
Jia Li ◽  
Da Min Zhang
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Steady State ◽  
Fast Fourier Transform ◽  
Power Quality ◽  
Detection System ◽  
Detection Algorithm ◽  
Detection Algorithms ◽  
Quality Detection ◽  
The Fourier Transform

Based on the comparative analysis of the fast Fourier transform (FFT), the short-time Fourier transform (STFT), the wavelet transform (WT) and other power quality detection algorithms, this paper puts forward to a new power quality detection algorithm which combines the Fourier transform with the wavelet transform. The transient as well as the steady state signals are separated on the basis that the wavelet transform is sensitive to the singular signals. The presented algorithm detects a variety of harmonic parameters of the gird after the separation of steady state signals is finished by fast Fourier transform. A new power quality detection system is then designed based on the core chip of S3C2440A, and the algorithm which is ARM-9 based is transplanted into the embedded Linux operating system to carry out the experiments. Analysis of the experimental data shows the detection algorithm is reliable by Fourier transform and wavelet transform.

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