Two-Dimensional Discrete Fourier Transform with Variable Parameter in the Spatial-Frequency Domain

2021 ◽  
Author(s):  
Olga Ponomareva ◽  
Alexey Ponomarev ◽  
Natalia Smirnova
Keyword(s):  
Fourier Transform ◽  
Spatial Frequency ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Variable Parameter ◽  
Two Dimensional ◽  
Spatial Frequency Domain

scholarly journals Sliding signal processing in telecommunication networks based on two-dimensional discrete Fourier transform

2019 ◽  
Vol 30 ◽  
pp. 04013
Author(s):  
Vladimir Ponomarev ◽  
Olga Ponomareva ◽  
Alexey Ponomarev ◽  
Natalya Smirnova
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Spatial Frequency ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Telecommunication Networks ◽  
Mathematical Representation ◽  
Two Dimensional ◽  
Discrete Signals ◽  
Spatial Frequency Domain

A method of vertical sliding processing of two-dimensional discrete signals in the spatial frequency domain is proposed — a method of fast vertically sliding two-dimensional discrete Fourier transform. The mathematical representation of the two-dimensional discrete Fourier transform in algebraic and matrix form is considered. An effective method of vertically sliding two-dimensional discrete Fourier transform is proposed. The algorithm developed in the framework of the proposed method allows calculating the coefficients (bins) of this transformation in real time.

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.

Two-Dimensional Velocity Data Smoothing and Structural Angular Velocity Extraction Using a DFT-IDFT Technique

1991 ◽  
Author(s):  
F. P. Sun ◽  
Larry D. Mitchell
Keyword(s):  
Fourier Transform ◽  
Spatial Frequency ◽  
Discrete Fourier Transform ◽  
Rotational Velocity ◽  
Dynamic Imaging ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Velocity Data ◽  
Data Set ◽  
Velocity Extraction

Abstract Structure dynamic imaging using a scanning Laser Doppler Velocimeter provides a feasible and efficient means for high-resolution rotational velocity extraction. It shifts the experimentalists’ ground from physical measurement of rotations to mathematical data manipulation and the differentiation of the experimental translational velocity. Consequently, the differentiability of velocity data becomes a major issue since such data are sequences of discrete numbers and are usually noise contaminated. This paper presents an effective method for two-dimensional data set smoothing using one-dimensional Discrete Fourier Transform-Inverse Discrete Fourier Transform (DFT-IDFT) process as a lowpass spatial filter. The angular velocities can then be defined analytically by differentiation in the spatial frequency domain. The technique is prototyped with several real experimental data sets from a steel plate excited at its resonance modes. Special attention is paid to the efforts on making 2-D data set periodic in the data frame as well as to the related error analysis. A preliminary criterion is suggested for determination of “spatial frequency truncation” in IDFT.

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