scholarly journals EM RESPONSE OF AN ARBITRARY SOURCE ON A LAYERED EARTH: A NEW COMPUTATIONAL APPROACH

Geophysics ◽  
1975 ◽  
Vol 40 (5) ◽  
pp. 773-789 ◽  
Author(s):  
J. Lajoie ◽  
J. Alfonso‐Roche ◽  
G. F. West
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Substantial Reduction ◽  
Theoretical Development ◽  
Electromagnetic Response ◽  
Fast Fourier Transform Algorithm ◽  
Large Area ◽  
Galvanic Current ◽  
Layered Earth ◽  
Rectangular Coordinates

The electromagnetic response of a layered earth is expressed in rectangular coordinates and the solution is obtained as a double inverse Fourier transform. This simplilfies the theoretical development for any EM source, grounded or not, and the fast Fourier transform algorithm may be used to evaluate the fields. In some cases where complicated source geometries are used and where the fields are required over a large area or volume, the procedure may lead to a substantial reduction in computation costs. The standard problems of the numerical fast Fourier transform algorithm may be overcome by using correction techniques such as pre‐aliasing. An analysis of the ground‐wire EM source shows that the infinite line is a poor approximation to the long grounded line due to the strong component of galvanic current in the ground.

SNOCRAFT: A Learning-Oriented Shorthand Notation for Creating, Representing, and Analyzing Fast Fourier Transform Algorithms

1980 ◽  
Vol 17 (3) ◽  
pp. 284-284
Author(s):  
Robert J. Meir ◽  
Sathyanarayan S. Rao
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fourier Transforms ◽  
Reduced Form ◽  
Fast Fourier Transform Algorithm ◽  
Signal Flow Graph ◽  
Shorthand Notation ◽  
The Matrix ◽  
Fourier Algorithm ◽  
Fft Analysis

This paper presents a full and well-developed view of the Fast Fourier Transform (FFT). It is intended for the reader who wishes to learn and develop his own fast Fourier algorithm. The approach presented here utilizes the matrix description of fast Fourier transforms. This approach leads to a systematic method for greatly reducing the complexity and the space required by variety of signal flow graph descriptions. This reduced form is called SNOCRAFT. From this representation, it is then shown how one can derive all possible fast Fourier transform algorithms, including the Weinograd Fourier transform algorithm. It is also shown from the SNOCRAFT representation that one can easily compute the number of multiplications and additions required to perform a specified fast Fourier transform algorithm. After an elementary introduction to matrix representation of fast Fourier transform algorithm, the method of generating all possible fast Fourier transform algorithms is presented in detail and is given in three sections. The first section discusses the Generation of SNOCRAFT and the second section illustrates how Operations on SNOCRAFT are made. These operations include inversion and rotation. The last section deals with the FFT Analysis. In this section, examples are provided to illustrate how one counts the number of multiplications and additions involved in performing the transform that one has developed.

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.

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