FFTFIL; a filtering program based on two-dimensional Fourier analysis of geophysical data

1983 ◽  
Author(s):  
T.G. Hildenbrand
Keyword(s):  
Fourier Analysis ◽  
Geophysical Data ◽  
Two Dimensional

FOURIER ANALYSIS OVER HYPERBOLIC ALGEBRA, PSEUDO-DIFFERENTIAL OPERATORS, AND HYPERBOLIC DEFORMATION OF CLASSICAL MECHANICS

2007 ◽  
Vol 10 (03) ◽  
pp. 421-438 ◽  
Author(s):  
ANDREI KHRENNIKOV
Keyword(s):  
Quantum Mechanics ◽  
Fourier Analysis ◽  
Poisson Bracket ◽  
Commutative Algebra ◽  
Differential Operators ◽  
Classical Mechanics ◽  
Complex Numbers ◽  
Two Dimensional ◽  
Quantum Deformation ◽  
Pseudo Differential Operators

We develop Fourier analysis over hyperbolic algebra (the two-dimensional commutative algebra with the basis e1 = 1, e2 = j, where j2 = 1). We demonstrated that classical mechanics has, besides the well-known quantum deformation over complex numbers, another deformation — so-called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit h → 0 not only of the ordinary Moyal bracket, but also a hyperbolic analogue of the Moyal bracket.

scholarly journals Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array

2021 ◽  
Vol 3 (1) ◽  
pp. 13-34
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Analysis ◽  
Fixed Points ◽  
Limit Cycles ◽  
Circular Cone ◽  
Two Dimensional ◽  
Periodic Functions ◽  
Fundamental Properties ◽  
Art And Architecture ◽  
The Trinity ◽  
Func Tion

Continually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time.

Two Dimensional Fourier Analysis

1995 ◽  
pp. 309-332
Author(s):  
Robert M. Gray ◽  
Joseph W. Goodman
Keyword(s):  
Fourier Analysis ◽  
Two Dimensional

Vernier Image Processing: Model and Experiments

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 110-110
Author(s):  
A V Chihman ◽  
V N Chihman ◽  
Y E Shelepin
Keyword(s):  
Fourier Analysis ◽  
Visual Processing ◽  
Fourier Spectrum ◽  
Field Size ◽  
Two Dimensional ◽  
Frequency Range ◽  
Additional Line ◽  
Point Spread ◽  
Model Predictions ◽  
Spread Function

Earlier we proposed a model for visual processing of the optical image of Vernier targets (1996 Perception25 Supplement, 115 – 116) based on Fourier analysis of the image. Our model comprises blurring of the thin Vernier bars by the optical point-spread function followed by calculation of the two-dimensional Fourier spectrum. In our model the processing area for Fourier analysis (the receptive field size) is 5 min arc. For a Vernier target, the contrast energy in the low-spatial-frequency range is different in different orientations, and magnification of the Vernier shift changes the orientation of the oblique Fourier components. To test the model, we carried out experiments in which the stimuli were Vernier lines with additional line distractors orthogonal to the orientation of the oblique Fourier components. Thresholds for detecting Vernier displacements were determined by a 2AFC paradigm and compared with model predictions. The results are consistent with our modelling of Vernier performance as a measurement of oblique components of the 2-D Fourier spectrum.

Fourier analysis of magnetophonon and two-dimensional Shubnikov-de Haas magnetoresistance structure

1975 ◽  
Vol 8 (7) ◽  
pp. 1034-1053 ◽  
Author(s):  
L Eaves ◽  
R A Hoult ◽  
R A Stradling ◽  
R J Tidey ◽  
J C Portal ◽  
...  
Keyword(s):  
Fourier Analysis ◽  
Two Dimensional
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