Optical implementation of the fractional Hilbert transform for two-dimensional objects

1997 ◽  
Vol 36 (26) ◽  
pp. 6620 ◽  
Author(s):  
A. W. Lohmann ◽  
E. Tepichín ◽  
J. G. Ramírez
Keyword(s):  
Hilbert Transform ◽  
Two Dimensional ◽  
Fractional Hilbert Transform

Fractional Hilbert transform and isotropic Hilbert transform for two-dimensional objects: numerical simulation

1999 ◽  
Author(s):  
M. Torres ◽  
Eduardo Tepichin-Rodriguez ◽  
Adolf W. Lohmann ◽  
David Sanchez ◽  
Gustavo Ramirez Zabaleta
Keyword(s):  
Numerical Simulation ◽  
Hilbert Transform ◽  
Two Dimensional ◽  
Fractional Hilbert Transform

Fractional Hilbert transform

1996 ◽  
Vol 21 (4) ◽  
pp. 281 ◽  
Author(s):  
Adolf W. Lohmann ◽  
David Mendlovic ◽  
Zeev Zalevsky
Keyword(s):  
Hilbert Transform ◽  
Fractional Hilbert Transform

scholarly journals Norm variation of ergodic averages with respect to two commuting transformations

2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE
Keyword(s):  
Harmonic Analysis ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Quantitative Result ◽  
Square Function ◽  
Two Dimensional ◽  
Ergodic Averages ◽  
Multilinear Singular Integrals

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

Theory of 2-D complex seismic trace analysis

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 264-272 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Trace Analysis ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Instantaneous Amplitude ◽  
Dip Angle

The ideas of 1-D complex seismic trace analysis extend readily to two dimensions. Two‐dimensional instantaneous amplitude and phase are scalars, and 2-D instantaneous frequency and bandwidth are vectors perpendicular to local wavefronts, each defined by a magnitude and a dip angle. The two independent measures of instantaneous dip correspond to instantaneous apparent phase velocity and group velocity. Instantaneous phase dips are aliased for steep reflection dips following the same rule that governs the aliasing of 2-D sinusoids in f-k space. Two‐dimensional frequency and bandwidth are appropriate for migrated data, whereas 1-D frequency and bandwidth are appropriate for unmigrated data. The 2-D Hilbert transform and 2-D complex trace attributes can be efficiently computed with little more effort than their 1-D counterparts. In three dimensions, amplitude and phase remain scalars, but frequency and bandwidth are 3-D vectors with magnitude, dip angle, and azimuth.

Use of the Hilbert transform to interpret self-potential anomalies due to two-dimensional inclined sheets

1990 ◽  
Vol 133 (1) ◽  
pp. 117-126 ◽  
Author(s):  
N. Sundararajan ◽  
I. Arun Kumar ◽  
N. L. Mohan ◽  
S. V. Seshagiri Rao
Keyword(s):  
Hilbert Transform ◽  
Two Dimensional ◽  
The Hilbert Transform ◽  
Self Potential
Sign in / Sign up

Export Citation Format

Share Document