Browsing by Keywords "Fractional Fourier transform"
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About the Wigner distribution of a graded index medium and the fractional fourier transform operation
(S P I E  International Society for Optical Engineering, 1993)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 ... 
Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence
(Elsevier, 200501)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
(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, Piscataway, NJ, United States, 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, 201509)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 ... 
Efficient algorithm to extract components of a composite signal
(IEEE (Institute of Electrical and Electronics Engineers), 2000)An efficient algorithm is proposed to extract components of a composite signal. The proposed approach has two stages of processing in which the timefrequency supports of the individual signal components are identified and ... 
Every Fourier optical system is equivalent to consecutive fractionalFourierdomain filtering
(Optical Society of America, 19960610)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 athorder fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zerothorder fractional Fourier transform operation is equal to the identity operation and the firstorder ... 
Fractional Fourier transform preprocessing for neural networks and its application to object recognition
(Pergamon Press, 2002)This study investigates fractional Fourier transform preprocessing of input signals to neural networks. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. ... 
Generalized timebandwidth product optimal shorttime fourier transformation
(2002)By extending the timebandwidth product concept to fractional Fourier domains, a generalized timebandwidth 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 crossterms
(Institute of Electrical and Electronics Engineers, 2000)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 phasespace representations
(Elsevier, 20010401)In this communication we propose performing twodimensional correlation operation between phasespace 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 ... 
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
(IEEE Computer Society, 2014)We study the degrees of freedom of optical systems and signals based on spacefrequency (phasespace) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the spacefrequency ... 
Optical implementation of the twodimensional fractional Fourier transform with different orders in the two dimensions
(Elsevier BV * NorthHolland, 19951015)Previous optical implementations of the twodimensional 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 image restoration with the fractional Fourier transform
(OSA  The Optical Society, 199804)The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for spaceinvariant degradation models and spaceinvariant signal and noise characteristics. For spacevarying degradations and ... 
Optimal representation and processing of optical signals in quadraticphase systems
(Elsevier, 2016)Optical fields propagating through quadraticphase 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 ... 
Shorttime Fourier transform: two fundamental properties and an optimal implementation
(IEEE, 2003)Shift and rotation invariance properties of linear timefrequency representations are investigated. It is shown that among all linear timefrequency representations, only the shorttime Fourier transform (STFT) family with ...