Optimal Filtering with Linear Canonical Transformations

Cataloged from PDF version of article.Optimal filtering with linear canonical transformations allows smaller mean-square errors in restoring signals degraded by linear time- or space-variant distortions and non-stationary noise. This reduction in error comes at no additional computational cost. This is made possible by the additional flexibility that comes with the three free parameters of linear canonical transformations, as opposed to the fractional Fourier transform which has only one free parameter, and the ordinary Fourier transform which has none. Application of the method to severely degraded images is shown to be significantly superior to filtering in fractional Fourier domains in certain cases

Complex signal recovery from multiple fractional Fourier-transform intensities

Cataloged from PDF version of article.The problem of recovering a complex signal from the magnitudes of any number of its fractional Fourier transforms at any set of fractional orders is addressed. This problem corresponds to the problem of phase retrieval from the transverse intensity profiles of an optical field at arbitrary locations in an optical system involving arbitrary concatenations of lenses and sections of free space. The dependence of the results on the number of orders, their spread, and the noise is investigated. Generally, increasing the number of orders improves the results, but with diminishing return beyond a certain point. Selecting the measurement planes such that their fractional orders are well separated or spread as much as possible also leads to better results. (c) 2005 Optical Society of Americ

Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence

Cataloged from PDF version of article.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 arbitrary locations along the optical axis. The convergence of the iterative algorithm, the effects of noise or measurement errors, and their dependence on the fractional transform order are investigated. It is observed that in general, better results are obtained when the fractional transform order is close to unity and poorer results are obtained when the order is close to zero. It follows that to the extent that conditions allow, the fractional order between the two measurement planes should be chosen as close to unity (or other odd integer) as possible for best results. (C) 2004 Elsevier B.V. All rights reserved

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

Perspective projections in the space-frequency plane and fractional Fourier transforms

Cataloged from PDF version of article.Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can he approximately modeled in terms of the fractional Fourier transform, The region of validity of the approximation is examined. Numerical examples are presented. (C) 2000 Optical Society of Americ

Convolution and Filtering in Fractional Fourier Domains

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon 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. © 1994, The Optical Society of Japan. All rights reserved

An optimized resilient advance bandwidth scheduling for media delivery services

Part 3: Evaluation and Experimental Study of Rich Network ServicesInternational audienceIn IP-based media delivery services, we often deal with predictable network load and traffic, making it beneficial to use advance reservations even when network failure occurs. In such a network, to offer reliable reservations, fault-tolerance related features should be incorporated in the advance reservation system. In this paper, we propose an optimized protection mechanism in which backup paths are selected in advance to protect the transfers when any failure happens in the network. Using a shared backup path protection, the proposed approach minimizes the backup capacity of the requests while guaranteeing 100% single link failure recovery. We have evaluated the quality and complexity of our proposed solution and the impact of different percentages of backup demands and timeslot sizes have been investigated in depth. The presented approach has been compared to our previously-designed algorithm as a baseline. Our simulation results reveal a noticeable improvement in request acceptance rate, up to 9.2%. Moreover, with fine-grained timeslot sizes and under limited network capacity, the time complexity of the proposed solution is up to 14% lower

Filtering in fractional Fourier domains and their relation to chirp transforms

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon 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

Signal recovery from partial fractional Fourier domain information and its applications

The problem of recovering signals from partial fractional Fourier transform information arises in wave propagation problems where the measured information is partial, spread over several observation planes, or not of sufficient spatial resolution or accuracy. This problem can be solved with the method of projections onto convex sets, with the convergence of the iterative algorithm being assured. Several prototypical application scenarios and simulation examples are presented. © The Institution of Engineering and Technology 2008

Supervised Human-Guided Data Exploration

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