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Lineshape analysis is a recurrent and often computationally intensive task in optics, even more so for multiple peaks in the presence of noise. We demonstrate an algorithm which takes advantage of peak multiplicity (N) to retrieve line shape information. The method is exemplified via analysis of Lorentzian and Gaussian contributions to individual lineshapes for a practical spectroscopic measurement and benefits from a linear increase in sensitivity with the number N. The robustness of the method and its benefits in terms of noise reduction and order of magnitude improvement in run-time performance are discussed., 12 pages, 6 figures

Surfing in rough waters is not always as fun as wave riding the &ldquo, big one&rdquo, Similarly, in optimization problems, fitness landscapes with a huge number of local optima make the search for the global optimum a hard and generally annoying game. Computational Intelligence optimization metaheuristics use a set of individuals that &ldquo, surf&rdquo, across the fitness landscape, sharing and exploiting pieces of information about local fitness values in a joint effort to find out the global optimum. In this context, we designed surF, a novel surrogate modeling technique that leverages the discrete Fourier transform to generate a smoother, and possibly easier to explore, fitness landscape. The rationale behind this idea is that filtering out the high frequencies of the fitness function and keeping only its partial information (i.e., the low frequencies) can actually be beneficial in the optimization process. We prove our theory by combining surF with a settings free variant of Particle Swarm Optimization (PSO) based on Fuzzy Logic, called Fuzzy Self-Tuning PSO. Specifically, we introduce a new algorithm, named F3ST-PSO, which performs a preliminary exploration on the surrogate model followed by a second optimization using the actual fitness function. We show that F3ST-PSO can lead to improved performances, notably using the same budget of fitness evaluations.

We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and structural properties of several quasianalytic spaces of functions and ultradistributions. In particular, our results apply to Fourier hyperfunctions and Fourier ultra-hyperfunctions., 37 pages

When seismic waves propagate through the Earth, their high-frequency energy is absorbed by subsurface viscoelastic media. Seismic wavelet appears to be stretched out, as it is dominated by low-frequency components. In order to enhance seismic resolution, we propose here a wavelet compression method that utilizes the scale characteristic in the Fourier transform. The novelty of the scheme is a frequency-dependent scaling that extends the amplitude spectrum to both high- and low-frequency axes simultaneously. This is for the first time to make this frequency-dependent proposal, instead of a constant scaling scheme in the classic Fourier theory. It compresses seismic wavelet in the time domain, and also simplifies the wavelet form effectively. This frequency-dependent scaling scheme leads to a transferring filter that is applicable to seismic field data. It results in an improvement in data resolution and in the ability of thin-layer identification, which will facilitate further seismic inversion and reservoir characterization.

Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, low-pass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: (1) sampling with arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels and, (3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel and Fractional Fourier domain based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short time SAFT, and study convolution theorems that establish a convolution--multiplication property in the SAFT domain., 42 pages, 3 figures, manuscript under review

International audience; The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic dual-ity between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral.

We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump L\'evy processes. Combined with the Burkholder-Gundy inequalities, it gives the $L^p$ two-way boundedness, for $1, Comment: 17 pages

The fractional fourier transform can be viewed as a generalization of the Fourier transform. The relation between rotation of a signal in the time-frequency plane to the Fractional Fourier tranform is introduced. In this paper, the fractional Fourier transform and its properties are presented. Further the problem of finding an optimum fractional Fourier Domain, i.e...... one in which the energy of a signal is maximally concentrated, is discussed for quadratic chirps. A quadratic chirp is a signal whose frequency bears a quadratic relation in time.

A theoretical foundation to the notion of 2D transform and 2D signal processing is given, focusing on 2D group-based transforms, of which the 2D Haar and 2D Fourier transforms are particular instances. Conditions for separability of these transforms are established. The theory is applied to certain groups that are wreath products of cyclic groups to give separable and inseparable 2D wreath product transforms and their filter bank implementations. © 2003 Published by Elsevier Ltd.

A Fourier transform akin to Sneddon's R -transform is introduced. It is shown that the Hilbert transform links the two in much the same way as it connects the classical Fourier sine and cosine transforms.

Molecular and macromolecular structure analysis by high resolution and accurate mass spectrometry (MS) is indispensable for a number of fundamental and applied research areas, including health and energy domains. Comprehensive structure analysis of molecules and macromolecules present in the extremely complex samples and performed under time-constrained experimental conditions demands a substantial increase in the acquisition speed of high resolution MS data. We demonstrate here that signal processing based on the filter diagonalization method (FDM) provides the required resolution for shorter experimental transient signals in ion cyclotron resonance (ICR) MS compared to the Fourier transform (FT) processing. We thus present the development of a FDM-based MS (FDM MS) and demonstrate its implementation in ICR MS. The considered FDM MS applications are in bottom-up and top-down proteomics, metabolomics, and petroleomics.

ACL-11-01; International audience; Quantifying and monitoring the structure and degradation of tropical forests over regional to global scales is gaining increasing scientific and societal importance. Reliable automated methods are only beginning to appear; for instance, through the recent development of textural approaches applied to high resolution optical imagery. In particular, the Fourier Transform Textural Ordination (FOTO) method shows some potential to provide non-saturating estimates of tropical forest structure, including for large scale applications. However, we need to understand more precisely how canopy structure interacts with physical signals (light) to produce a given texture, notably to assess the method's sensitivity to varying sun-view acquisition conditions. In this study, we take advantage of the detailed description of canopy topography provided by airborne small footprint LiDAR data acquired over the Paracou forest experimental station in French Guiana. Using hillshade models and a range of sun-view angles identical to the actual parameter distributions found for Quickbird™ images over the Amazon, we study noise and bias in texture estimation induced by the changing configurations. We introduce the bidirectional texture function, which summarizes these effects, and in particular the existence of a textural ‘hot spot', similar to a well-known feature of bidirectional reflectance studies. For texture, this effect implies that coarseness decreases in configurations for which shadows are concealed to the observer. We also propose a method, termed partitioned standardization, that allows mitigating acquisition effects and discuss the potential for an operational use of VHR optical imagery and the FOTO method in the current context of international decisions to reduce CO2 emissions due to deforestation and forest degradation

The TT-transform stands for time–time transform and has been derived as an inverse Fourier transform of the time-frequency -transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform, This work was supported by the project SigSensual ref. REN2003-08341-C03- C01-02 and CTM2004-04510-C03-02. The work of M. Schimmel is supported through the Ramon y Cajal and the Consolider-Ingenio 2010 Nr. CSD2006-00041 program.

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.

The optical and digital implementations of general linear systems are costly. Through several examples we show that either exact realizations or useful approximations of these systems may be implemented in the form of repeated-filtering operations in consecutive fractional Fourier domains. These implementations are much cheaper than direct implementations of general linear systems. Thus we may significantly decrease the implementation costs of general linear systems with little or no decrease in performance by synthesizing them with the proposed repeated-filtering method. (C) 1998 Optical Society of America.

An analysis of the first harmonic components of the sequence resulting from a suitable deconvolution operation on a response composed of single partially overlapped signals allows the resolution of the over-all response into the individual signals. Ideally, it is possible to reduce the original response to single impulses with suitable height and location. If the number, n, of single signals is known, the first n– 1 harmonic components of the spectrum of the deconvoluted response, plus the continuous term, need only be computed. On the other hand, if the over-all response includes an unknown number of single signals, a method is suggested that requires the calculation of only a few harmonic components in order to build up a suitable form of the whole spectrum of the deconvoluted signal. The effectiveness of the proposed procedures, which are suitable for the treatment of responses from different analytical techniques, was tested on simulated responses, both in the absence and presence of noise, and on experimental data, viz., differential-pulse polarographic responses recorded on solutions containing two metals that were reduced at similar potentials.

We introduce a new class of fast algorithms for the application to arbitrary vectors of certain special function transforms. The scheme is applicable to a number of transforms, including the Fourier–Bessel transform, the non-equispaced Fourier transform, transforms associated with all classical orthogonal polynomials, etc.; it requires order O ( n log ( n ) ) operations to apply an n × n matrix to an arbitrary vector. The performance of the algorithm is illustrated by several numerical examples.

We propose a new method for the accurate estimation of nonlinear response of the PZT to the applied voltage. The method uses discrete chirp Fourier transform for the coarse estimation followed by a fine search method for the accurate estimation of the phase step and nonlinearity. The method can be extended to the cases of extraction of multiple phases in the configurations involving multiple PZTs such as holographic moire in the presence of nonlinearity. The robustness of the proposed method is verified by comparing with Cramer-Rao lower bound. Experimental results prove the method's feasibility. (c) 2006 Elsevier B.V. All rights reserved.