Now showing items 1-20 of 24

• #### About the Wigner distribution of a graded index medium and the fractional fourier transform operation ﻿

(SPIE, 1993-08)
Upon propagation through quadratic graded index media, the Wigner distribution of the wavefunction of light rotates uniformly. As a consequence, a definition of fractional Fourier transforms based on rotating the functions ...
• #### Applications of the fractional Fourier transform in optics and signal processing-a review ﻿

(SPIE, 1996)
The fractional Fourier transform The fractional Fourier transform is a generalization of the common Fourier transform with an order parameter a. Mathematically, the ath order fractional Fourier transform is the ath power ...
• #### Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence ﻿

(Elsevier, 2005-01)
The problem of recovering a complex signal from the magnitudes of two of its fractional Fourier transforms is addressed. This corresponds to phase retrieval from the transverse intensity profiles of an optical field at two ...
• #### Diffraction and holography from a signal processing perspective ﻿

(SPIE, 2006)
The fact that plane waves are solutions of the Helmholtz equation in free space allows us to write the exact solution to the diffraction problem as a superposition of plane waves. The solution of other related problems can ...
• #### The discrete fractional Fourier transformation ﻿

(IEEE, 1996)
Based on the fractional Fourier transformation of sampled periodic functions, the discrete form of the fractional Fourier transformation is obtained. It is found that only for a certain dense set of fractional orders such ...
• #### The effect of distribution of information on recovery of propagating signals ﻿

(Bilkent University, 2015-09)
Interpolation is one of the fundamental concepts in signal processing. The analysis of the di fficulty of interpolation of propagating waves is the subject of this thesis. It is known that the information contained in a ...
• #### An efficient algorithm to extract components of a composite signal ﻿

(IEEE, 2000)
An efficient algorithm is proposed to extract components of a composite signal. The proposed approach has two stages of processing in which the time-frequency supports of the individual signal components are identified and ...
• #### Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering ﻿

(Optical Society of America, 1996-06-10)
We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) ...
• #### Feature extraction with the fractional Fourier transform ﻿

(Bilkent University, 1998)
In this work, alternative design and implementation techniques for feature extraction applications are proposed. The proposed techniques amount to decomposing the overall feature extraction problem into a global linear ...
• #### The Fractional Fourier transform and harmonic oscillation ﻿

(Springer, 2002)
The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order ...
• #### Generalized time-bandwidth product optimal short-time fourier transformation ﻿

(IEEE, 2002-05)
By extending the time-bandwidth product concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is introduced. The GTBP provides a rotation independent measure for the support of the signals in ...
• #### High resolution time frequency representation with significantly reduced cross-terms ﻿

(IEEE, 2000-06)
A novel algorithm is proposed for efficiently smoothing the slices of the Wigner distribution by exploiting the recently developed relation between the Radon transform of the ambiguity function and the fractional Fourier ...
• #### Improved acoustics signals discrimination using fractional Fourier transform based phase-space representations ﻿

(Elsevier, 2001-04-01)
In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical ...
• #### Interpolating between periodicity and discreteness through the fractional Fourier transform ﻿

(IEEE, 2006)
Periodicity and discreteness are Fourier duals in the same sense as operators such as coordinate multiplication and differentiation, and translation and phase shift. The fractional Fourier transform allows interpolation ...
• #### Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions ﻿

(Elsevier BV * North-Holland, 1995-10-15)
Previous optical implementations of the two-dimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present ...
• #### Optimal fractional fourier filtering for graph signals ﻿

(IEEE, 2021-05-19)
Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. ...
• #### Optimal image restoration with the fractional Fourier transform ﻿

(OSA - The Optical Society, 1998-04)
The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for space-invariant degradation models and space-invariant signal and noise characteristics. For space-varying degradations and ...
• #### Optimal representation and processing of optical signals in quadratic-phase systems ﻿

(Elsevier, 2016)
Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. ...
• #### Resolution enhancement of low resolution wavefields with POCS algorithm ﻿

(The Institution of Engineering and Technology, 2003)
The problem of enhancing the resolution of wavefield or beam profile measurements obtained using low resolution sensors is addressed by solving the problem of interpolating signals from partial fractional Fourier transform ...
• #### Short-time Fourier transform: two fundamental properties and an optimal implementation ﻿

(IEEE, 2003)
Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with ...