9,864 research outputs found
Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering
Cataloged from PDF version of article.Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform
stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters inserted between
appropriately scaled ordinary Fourier transform stages. Thus every operation that can be accomplished by repeated
filtering in fractional Fourier domains can also be accomplished by repeated filtering alternately in the ordinary time and
frequency domains
Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
Cataloged from PDF version of article.A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing
Estimation, Analysis and Smoothing of Self-Similar Network Induced Delays in Feedback Control of Nuclear Reactors
This paper analyzes a nuclear reactor power signal that suffers from network
induced random delays in the shared data network while being fed-back to the
Reactor Regulating System (RRS). A detailed study is carried out to investigate
the self similarity of random delay dynamics due to the network traffic in
shared medium. The fractionality or selfsimilarity in the network induced delay
that corrupts the measured power signal coming from Self Powered Neutron
Detectors (SPND) is estimated and analyzed. As any fractional order randomness
is intrinsically different from conventional Gaussian kind of randomness, these
delay dynamics need to be handled efficiently, before reaching the controller
within the RRS. An attempt has been made to minimize the effect of the
randomness in the reactor power transient data with few classes of smoothing
filters. The performance measure of the smoothers with fractional order noise
consideration is also investigated into.Comment: 6 pages, 6 figure
Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform
Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We
propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the
level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators
Repeated filtering in consecutive fractional Fourier domains
Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 1997.Thesis (Ph. D.) -- Bilkent University, 1997.Includes bibliographical references leaves 96-105.In the first part of this thesis, relationships between the fractional Fourier
transformation and Fourier optical systems are analyzed to further elucidate
the importance of this transformation in optics. Then in the second part, the
concept of repeated filtering is considered. In this part, the repeated filtering
method is interpreted in two different ways. In the first interpretation the
linear transformation between input and output is constrained to be of the
form of repeated filtering in consecutive domains. The applications of this
constrained linear transformation to signal synthesis (beam shaping) and signal
restoration are discussed. In the second interpretation, general linear systems are
synthesized with repeated filtering in consecutive domains, and the synthesis of
some important linear systems in signal processing and the .synthesis of optical
interconnection architectures are considered for illustrative purposes. In all of the
examples, when our repeated filtering method is compared with single domain
filtering methods, significant improvements in performance are obtained with
only modest increases in optical or digital implementation costs. Similarly, when
the proposed method is compared with general linear systems, it is seen that
acceptable performance may be possible with significant computational savings
in implementation costs.Erden, M FatihPh.D
Chirp filtering in the fractional Fourier Domain
Cataloged from PDF version of article.In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta
function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of
the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the
FRT is used for filtering the line delta function in the appropriate fractional Fourier domain.
Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved
Generalized filtering configurations with applications in digital and optical signal and image processing
Ankara : Department of Electrical and Electonics Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1999.Thesis (Ph.D.) -- Bilkent University, 1999.Includes bibliographical refences.In this thesis, we first give a brief summary of the fractional Fourier transform which
is the generalization of the ordinary Fourier transform, discuss its importance in
optical and digital signal processing and its relation to time-frequency representations.
We then introduce the concept of filtering circuits in fractional Fourier domains.
This concept unifies the multi-stage (repeated) and multi-channel (parallel) filtering
configurations which are in turn generalizations of single domain filtering in fractional
Fourier domains. We show that these filtering configurations allow a cost-accuracy tradeoff
by adjusting the number of stages or channels. We then consider the application
of these configurations to three important problems, namely system synthesis, signal
synthesis, and signal recovery, in optical and digital signal processing. In the system
and signal synthesis problems, we try to synthesize a desired system characterized by its
kernel, or a desired signal characterized by its second order statistics by using fractional
Fourier domain filtering circuits. In the signal recovery problem, we try to recover or
estimate a desired signal from its degraded version. In all of the examples we give,
significant improvements in performance are obtained with respect to single domain
filtering methods with only modest increases in optical or digital implementation costs.
Similarly, when the proposed method is compared with the direct implementation of
general linear systems, we see that significant computational savings are obtained with
acceptable decreases in performance.Kutay, Mehmet AlperPh.D
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