On: “A Method to minimize edge effects in two‐dimensional discrete Fourier transforms” by Yanick Ricard and Richard J. Blakely (GEOPHYSICS, 53, 1113–1117, August 1988).

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1514-1514 ◽  
Author(s):  
Kenneth F. Sprenke
Keyword(s):  
Continuous Spectrum ◽  
Edge Effects ◽  
Fourier Transforms ◽  
Interpolation Process ◽  
Two Dimensional ◽  
Discrete Fourier Transforms ◽  
Sampling Grid ◽  
Valuable Method ◽  
Sampling Window ◽  
Rotational Transform

The authors of this paper have created a very valuable method for approximating the two‐dimensional continuous spectrum by repeatedly rotating a rectangular sampling grid and averaging the resulting spectra. The authors state that their rotational transform “eliminates artifacts associated with the orientation of the rectangular sampling window.” However, I believe that one aspect of their method, the interpolation process, actually creates artifacts:

scholarly journals Theoretical foundations of digital vector Fourier analysis of two-dimensional signals padded with zero samples

2021 ◽  
pp. 55-65
Author(s):  
Olga Ponomareva ◽  
Aleksey Ponomarev
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Discrete Fourier Transform ◽  
Fourier Transforms ◽  
Information Control ◽  
Two Dimensional ◽  
Negative Effects ◽  
Variable Parameters ◽  
Discrete Fourier Transforms ◽  
Fourier Matrix

Introduction: The practice of using Fourier-processing of finite two-dimensional signals (including images), having confirmed its effectiveness, revealed a number of negative effects inherent in it. A well-known method of dealing with negative effects of Fourier-processing is padding signals with zeros. However, the use of this operation leads to the need to provide information control systems with additional memory and perform unproductive calculations. Purpose: To develop new discrete Fourier transforms for efficient and effective processing of two-dimensional signals padded with zero samples. Method: We have proposed a new method for splitting a rectangular discrete Fourier transform matrix into square matrices. The method is based on the application of the modulus comparability relation to order the rows (columns) of the Fourier matrix. Results: New discrete Fourier transforms with variable parameters were developed, being a generalization of the classical discrete Fourier transform. The article investigates the properties of Fourier transform bases with variable parameters. In respect to these transforms, the validity has been proved for the theorems of linearity, shift, correlation and Parseval's equality. In the digital spectral Fourier analysis, the concepts of a parametric shift of a two-dimensional signal, and a parametric periodicity of a two-dimensional signal have been introduced. We have estimated the reduction of the required memory size and the number of calculations when applying the proposed transforms, and compared them with the discrete Fourier transform. Practical relevance: The developed discrete Fourier transforms with variable parameters can significantly reduce the cost of Fourier processing of two-dimensional signals (including images) padded with zeros.

A method to minimize edge effects in two‐dimensional discrete Fourier transforms

Geophysics ◽  
1988 ◽  
Vol 53 (8) ◽  
pp. 1113-1117 ◽  
Author(s):  
Yanick Ricard ◽  
Richard J. Blakely
Keyword(s):  
Fourier Transforms ◽  
Earth Science ◽  
Gravity Data ◽  
Power Spectra ◽  
Magnetic Data ◽  
Moho Depth ◽  
Two Dimensional ◽  
Science Data ◽  
Discrete Fourier Transforms ◽  
Earth Science Data

Fourier transforms are widely used in analysis of two‐dimensional (2-D) earth‐science data, such as gravity and magnetic surveys, topographic models, and remote‐sensing images. For example, manipulations of gridded magnetic or gravity data, such as upward and downward continuation, reduction to the pole, wavelength filters, pseudogravity transformation, and vertical derivatives (Hildenbrand, 1983), are greatly simplified with Fourier transforms, as are certain forward and inverse calculations (Parker, 1973; Parker and Huestis, 1974). Power spectra computed from 2-D Fourier transforms are used to estimate depth to the top and bottom of magnetic sources from gridded magnetic data (Spector and Grant, 1970; Connard et al., 1983) and to estimate lithospheric strength and Moho depth from gridded gravity data (Dorman and Lewis, 1970; Louden and Forsyth, 1982; McNutt, 1983).

scholarly journals Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps

2017 ◽  
Vol 93 (3) ◽  
pp. 323-333 ◽  
Author(s):  
Fabian L. Kriegel ◽  
Ralf Köhler ◽  
Jannike Bayat-Sarmadi ◽  
Simon Bayerl ◽  
Anja E. Hauser ◽  
...  
Keyword(s):  
Cell Shape ◽  
Fourier Transforms ◽  
Self Organizing Maps ◽  
Discrete Fourier Transforms ◽  
Shape Characterization ◽  
Self Organizing

scholarly journals High-Bandpass Filters in Electrocardiography: Source of Error in the Interpretation of the ST Segment

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
F. Buendía-Fuentes ◽  
M. A. Arnau-Vives ◽  
A. Arnau-Vives ◽  
Y. Jiménez-Jiménez ◽  
J. Rueda-Soriano ◽  
...  
Keyword(s):  
Real Time ◽  
Fourier Transforms ◽  
Pass Filter ◽  
Discrete Fourier Transforms ◽  
Real Time Mode ◽  
Asymptomatic Patients ◽  
St Segment ◽  
Coronary Syndromes ◽  
Clinically Significant ◽  
High Pass

Introduction. Artifactual variations in the ST segment may lead to confusion with acute coronary syndromes. Objective. To evaluate how the technical characteristics of the recording mode may distort the ST segment. Material and Method. We made a series of electrocardiograms using different filter configurations in 45 asymptomatic patients. A spectral analysis of the electrocardiograms was made by discrete Fourier transforms, and an accurate recomposition of the ECG signal was obtained from the addition of successive harmonics. Digital high-pass filters of 0.05 and 0.5 Hz were used, and the resulting shapes were compared with the originals. Results. In 42 patients (93%) clinically significant alterations in ST segment level were detected. These changes were only seen in “real time mode” with high-pass filter of 0.5 Hz. Conclusions. Interpretation of the ST segment in “real time mode” should only be carried out using high-pass filters of 0.05 Hz.

Sign in / Sign up

Export Citation Format

Share Document