scholarly journals Appendix C: The Discrete-Time Fourier Transform, The Discrete Fourier Transform and The Fast Fourier Transform

2006 ◽  
pp. 391-396
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time

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 Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

2020 ◽  
Vol 149 ◽  
pp. 02010 ◽  
Author(s):  
Mikhail Noskov ◽  
Valeriy Tutatchikov
Keyword(s):  
Fourier Transform ◽  
Numerical Experiment ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Satellite Data ◽  
Digital Image ◽  
Digital Images ◽  
Two Dimensional ◽  
Fast Fourier Transform Algorithm

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

scholarly journals Gabor frames with trigonometric spline dual windows

2015 ◽  
Vol 08 (04) ◽  
pp. 1550072 ◽  
Author(s):  
Inmi Kim
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Higher Dimensions ◽  
Gabor Frames ◽  
One Dimension ◽  
Trigonometric Spline

A dual Gabor window pair has two functions that can reconstruct any function in [Formula: see text] using certain systems of their modulated and translated forms. Few explicit examples of dual Gabor window pairs are known. This paper constructs explicit examples with trigonometric form in one dimension as well as higher dimensions. Also, in the discrete time domain, the trigonometric form allows us to evaluate the Gabor coefficients efficiently using the Discrete Fourier Transform. The windows have fixed support and arbitrary smoothness.

Single-Rate Discrete-Time Signals and Systems

2009 ◽  
pp. 1-22
Author(s):  
Ljiljana Milic
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Transform Domain ◽  
Concise Review ◽  
Discrete Signals ◽  
Time Signals ◽  
The Time Domain

This chapter is a concise review of time-domain and transform-domain representations of single-rate discrete-time signals and systems. We consider first the time-domain representation of discrete-time signals and systems. The representation in transform domain comprises the discrete-time Fourier transform (DTFT), the discrete Fourier transform (DFT), and the z-transform. The basic realization structures for FIR and IIR systems are briefly described. Finally, the relations between continuous and discrete signals are given.

scholarly journals R–DFT-based Parameter Estimation for WiGig

2017 ◽  
Vol 61 (2) ◽  
pp. 224
Author(s):  
Barna Csuka ◽  
Zsolt Kollár
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Parameter Estimation ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Low Complexity ◽  
Estimation Methods ◽  
Ieee 802.11Ad ◽  
Parameter Estimation Methods ◽  
Processing Architecture

In this paper we present parameter estimation methods for IEEE 802.11ad transmission to estimate the frequency offset value and channel impulse response. Furthermore a less known low complexity signal processing architecture – the Recursive Discrete Fourier Transform (R-DFT) – is applied which may improve the estimation results. The paper also discusses the R-DFT and its advantages compared to the conventional Fast Fourier Transform.

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