Connection Between the Discrete Fourier Transform and the Fourier Transform.

2017 ◽  
pp. 85-92
Author(s):  
Valery Serov
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
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.

scholarly journals How can the Fourier Transform be Used in Radio Astronomy to Perform Spectral Analysis of Pulsars

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Pranesh Kumar ◽  
Arthur Western
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Low Frequency ◽  
Radio Frequency Interference ◽  
Radio Waves ◽  
Folding Algorithm ◽  
Radio Signals ◽  
Multiple Characteristics ◽  
The Fourier Transform

The analysis of pulsars is a complicated procedure due to the influence of background radio waves. Special radio telescopes designed to detect pulsar signals have to employ many techniques to reconstruct interstellar signals and determine if they originated from a pulsating radio source. The Discrete Fourier Transform on its own has allowed astronomers to perform basic spectral analysis of potential pulsar signals. However, Radio Frequency Interference (RFI) makes the process of detecting and analyzing pulsars extremely difficult. This has forced astronomers to be creative in identifying and determining the specific characteristics of these unique rotating neutron stars. Astrophysicists have utilized algorithms such as the Fast Fourier Transform (FFT) to predict the spin period and harmonic frequencies of pulsars. However, FFT-based searches cannot be utilized alone because low-frequency pulsar signals go undetected in the presence of background radio noise. Astrophysicists must stack up pulses using the Fast Folding Algorithm (FFA) and utilize the coherent dedispersion technique to improve FFT sensitivity. The following research paper will discuss how the Discrete Fourier Transform is a useful technique for detecting radio signals and determining the pulsar frequency. It will also discuss how dedispersion and the pulsar frequency are critical for predicting multiple characteristics of pulsars and correcting the influence of the Interstellar Medium (ISM).

The Agorithm Based on the Discrete Fourier Transform of Eye Detecting and Locating

2013 ◽  
Vol 680 ◽  
pp. 521-525
Author(s):  
Shu Wei Qu ◽  
Zhi Hong Guo ◽  
Fan Wang
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Facial Image ◽  
Operation Speed ◽  
Facial Information ◽  
Facial Characteristic ◽  
Exact Position ◽  
Accurate Position ◽  
Simulation Results ◽  
The Fourier Transform

Fatigue has a serious influence on people’s production and life. In this paper, which using the discrete Fourier transform algorithm to segment and extract person's facial image, so we can have a effective monitoring of people’s fatigue state base on the facial characteristic. With the help of the parameters characteristic of the Fourier transform, we can extract the key facial information from the image and achieve accurate position of the eyes. Simulation results show that the use of discrete Fourier transform to the exact position of the human eye, having a greatly improve on the operation speed of the eyes position system, and improving its accuracy and robustness.

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.

scholarly journals There Is Only One Fourier Transform

2017 ◽  
Author(s):  
Jens V. Fischer
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Fourier Transforms ◽  
Periodic Functions ◽  
Distributional Sense ◽  
Integral Fourier Transform ◽  
The Fourier Transform

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.

scholarly journals Four Particular Cases of the Fourier Transform

2018 ◽  
Author(s):  
Jens V. Fischer
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Fourier Transforms ◽  
Summation Formula ◽  
Periodic Functions ◽  
Tempered Distributions ◽  
Integral Fourier Transform ◽  
The Fourier Transform

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

scholarly journals Comparison of the Least-Squares Regression Line and a Truncated Discrete Fourier Transform when describing Linearly Correlated data

2020 ◽  
Author(s):  
Chris Anto
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Discrete Fourier Transform ◽  
Regression Line ◽  
Correlated Data ◽  
Least Squares Regression ◽  
Primary Method ◽  
The Fourier Transform

For long, the least squares regression line has been a primary method to analyze linearly correlated data. In this paper, the author suggests a method involving the Fourier transform that achieves evreything the regression line achieves-- and more

scholarly journals Comparison of the Least-Squares Regression Line and a Truncated Discrete Fourier Transform when describing Linearly Correlated data

2020 ◽  
Author(s):  
Chris Anto
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Discrete Fourier Transform ◽  
Regression Line ◽  
Correlated Data ◽  
Least Squares Regression ◽  
Primary Method ◽  
The Fourier Transform

For long, the least squares regression line has been a primary method to analyze linearly correlated data. In this paper, the author suggests a method involving the Fourier transform that achieves evreything the regression line achieves-- and more

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