26,281 research outputs found
The fractional Fourier domain decomposition
Cataloged from PDF version of article.We introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of
the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation
of space-variant linear systems. (c) 1999 Published by Elsevier Science B.V. All rights reserved
Discrete Fourier Transforms of Fractional Processes
Discrete Fourier transforms (dft's) of fractional processes are studied and an exact representation of the dft is given in terms of the component data. The new representation gives the frequency domain form of the model for a fractional process, and is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d >= 1/2. Various asymptotic approximations are suggested. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter dDiscrete Fourier transform, fractional Brownian motion; fractional integration; nonstationarity, operator decomposition, semiparametric estimation, Whittle likelihood
Fractional Fourier domain decomposition
We introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems
Continuous and discrete fractional Fourier domain decomposition
We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems
Image processing with the fractional Fourier transform: synthesis, compression and perspective projections
Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 2000.Thesis (Master's) -- Bilkent University, 2000.Includes bibliographical references leaves 50-55In this work, first we give a summary of the fractional Fourier transform
including its definition, important properties, generalization to two-dimensions
and its discrete counterpart. After that, we repeat the concept of filtering in
the fractional Fourier domains and give multi-stage and multi-channel filtering
configurations. Due to the nonlinear nature of the problem, the transform
orders in fractional Fourier domain filtering configurations have usually not
been optimized but chosen uniformly up to date. We discuss the optimization
of orders in the multi-channel filtering configuration. In the next part of this
thesis, we discuss the application of fractional Fourier transform based filtering
configurations to image representation and compression. Next, we introduce the
fractional Fourier domain decomposition for continuous signals and systems. In
the last part, we analyse perspective projections in the space-frequency plane
and show that under certain conditions they can be approximately modeled in
terms of the fractional Fourier transform.Yetik, I ŞamilM.S
Using EMD-FrFT filtering to mitigate high power interference in chirp tracking radars
This letter presents a new signal processing subsystem for conventional monopulse tracking radars that offers an improved solution to the problem of dealing with manmade high power interference (jamming). It is based on the hybrid use of empirical mode decomposition (EMD) and fractional Fourier transform (FrFT). EMD-FrFT filtering is carried out for complex noisy radar chirp signals to decrease the signal's noisy components. An improvement in the signal-to-noise ratio (SNR) of up to 18 dB for different target SNRs is achieved using the proposed EMD-FrFT algorithm
Self-similar prior and wavelet bases for hidden incompressible turbulent motion
This work is concerned with the ill-posed inverse problem of estimating
turbulent flows from the observation of an image sequence. From a Bayesian
perspective, a divergence-free isotropic fractional Brownian motion (fBm) is
chosen as a prior model for instantaneous turbulent velocity fields. This
self-similar prior characterizes accurately second-order statistics of velocity
fields in incompressible isotropic turbulence. Nevertheless, the associated
maximum a posteriori involves a fractional Laplacian operator which is delicate
to implement in practice. To deal with this issue, we propose to decompose the
divergent-free fBm on well-chosen wavelet bases. As a first alternative, we
propose to design wavelets as whitening filters. We show that these filters are
fractional Laplacian wavelets composed with the Leray projector. As a second
alternative, we use a divergence-free wavelet basis, which takes implicitly
into account the incompressibility constraint arising from physics. Although
the latter decomposition involves correlated wavelet coefficients, we are able
to handle this dependence in practice. Based on these two wavelet
decompositions, we finally provide effective and efficient algorithms to
approach the maximum a posteriori. An intensive numerical evaluation proves the
relevance of the proposed wavelet-based self-similar priors.Comment: SIAM Journal on Imaging Sciences, 201
On fractional powers of singular perturbations of the Laplacian
We qualify a relevant range of fractional powers of the so-called Hamiltonian
of point interaction in three dimensions, namely the singular perturbation of
the negative Laplacian with a contact interaction supported at the origin. In
particular we provide an explicit control of the domain of such a fractional
operator and of its decomposition into regular and singular parts. We also
qualify the norms of the resulting singular fractional Sobolev spaces and their
mutual control with the corresponding classical Sobolev norms
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