Showing papers on "Fourier transform published in 2008"

Efficient subpixel image registration algorithms

Abstract: Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

Action MACH a spatio-temporal Maximum Average Correlation Height filter for action recognition

Abstract: In this paper we introduce a template-based method for recognizing human actions called action MACH. Our approach is based on a maximum average correlation height (MACH) filter. A common limitation of template-based methods is their inability to generate a single template using a collection of examples. MACH is capable of capturing intra-class variability by synthesizing a single Action MACH filter for a given action class. We generalize the traditional MACH filter to video (3D spatiotemporal volume), and vector valued data. By analyzing the response of the filter in the frequency domain, we avoid the high computational cost commonly incurred in template-based approaches. Vector valued data is analyzed using the Clifford Fourier transform, a generalization of the Fourier transform intended for both scalar and vector-valued data. Finally, we perform an extensive set of experiments and compare our method with some of the most recent approaches in the field by using publicly available datasets, and two new annotated human action datasets which include actions performed in classic feature films and sports broadcast television.

Spatio-temporal Saliency detection using phase spectrum of quaternion fourier transform

Abstract: Salient areas in natural scenes are generally regarded as the candidates of attention focus in human eyes, which is the key stage in object detection. In computer vision, many models have been proposed to simulate the behavior of eyes such as SaliencyToolBox (STB), neuromorphic vision toolkit (NVT) and etc., but they demand high computational cost and their remarkable results mostly rely on the choice of parameters. Recently a simple and fast approach based on Fourier transform called spectral residual (SR) was proposed, which used SR of the amplitude spectrum to obtain the saliency map. The results are good, but the reason is questionable.

Fault Detection in Induction Machines Using Power Spectral Density in Wavelet Decomposition

Abstract: Motor-current-signature analysis has been successfully used in induction machines for fault diagnosis. The method, however, does not always achieve good results when the speed or the load torque is not constant, because this causes variations on the motor-slip and fast Fourier transform problems appear due to a nonstationary signal. This paper proposes a new method for motor fault detection, which analyzes the spectrogram based on a short-time Fourier transform and a further combination of wavelet and power-spectral-density (PSD) techniques, which consume a smaller amount of processing power. The proposed algorithms have been applied to detect broken rotor bars as well as shorted turns. Besides, a merit factor based on PSD is introduced as a novel approach for condition monitoring, and a further implementation of the algorithm is proposed. Theoretical development and experimental results are provided to support the research.

Ptychography and Related Diffractive Imaging Methods

Abstract: Publisher Summary Ptychography is a nonholographic solution of the phase problem. It is a method for calculating the phase relationships among different parts of a scattered wave disturbance in a situation where only the magnitude (intensity or flux) of the wave can be physically measured. Its usefulness lies in its ability (like holography) to obtain images without the use of lenses, and hence to lead to resolution improvements and access to properties of the scattering medium that cannot be easily obtained from conventional imaging methods. The chapter discusses ptychography in the context of other phase-retrieval methods in both historical and conceptual terms. In an original and oblique approach to the phase problem, it was Hoppe who proposed the first version of the particular solution to the phase problem. The word “ptychography” was introduced to suggest a solution to the phase problem using the convolution theorem, or rather the “folding” of diffraction orders into one another via the convolution of the Fourier transform of a localized aperture or illumination function in the object plane. Apart from computers, the two most important experimental issues that affect ptychography, relate to the degree of coherence in the illuminating beam and the detector efficiency and dynamic range.

Breakdown of Fourier’s Law in Nanotube Thermal Conductors

Abstract: We present experimental evidence that the room temperature thermal conductivity (kappa) of individual multiwalled carbon and boron-nitride nanotubes does not obey Fourier's empirical law of thermal conduction. Because of isotopic disorder, kappa's of carbon nanotubes and boron-nitride nanotubes show different length dependence behavior. Moreover, for these systems we find that Fourier's law is violated even when the phonon mean free path is much shorter than the sample length.

Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope

Abstract: We demonstrate the use of an ordinary white-light microscope for the study of the q-dependent dynamics of colloidal dispersions. Time series of digital video images are acquired in bright field with a fast camera, and image differences are Fourier analyzed as a function of the time delay between them. This allows for the characterization of the particle dynamics independent of whether or not they can be resolved individually. The characteristic times are measured in a wide range of wave vectors and the results are found to be in good agreement with the theoretically expected values for Brownian motion in a viscous medium.

Estimating Granger causality from fourier and wavelet transforms of time series data.

Abstract: Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.

FFTs on the Rotation Group

Abstract: We discuss an implementation of an efficient algorithm for the numerical computation of Fourier transforms of bandlimited functions defined on the rotation group SO(3). The implementation is freely available on the web. The algorithm described herein uses O(B 4) operations to compute the Fourier coefficients of a function whose Fourier expansion uses only (the O(B 3)) spherical harmonics of degree at most B. This compares very favorably with the direct O(B 6) algorithm derived from a basic quadrature rule on O(B 3) sample points. The efficient Fourier transform also makes possible the efficient calculation of convolution over SO(3) which has been used as the analytic engine for some new approaches to searching 3D databases (Funkhouser et al., ACM Trans. Graph. 83–105, [2003]; Kazhdan et al., Eurographics Symposium in Geometry Processing, pp. 167–175, [2003]). Our implementation is based on the “Separation of Variables” technique (see, e.g., Maslen and Rockmore, Proceedings of the DIMACS Workshop on Groups and Computation, pp. 183–237, [1997]). In conjunction with techniques developed for the efficient computation of orthogonal polynomial expansions (Driscoll et al., SIAM J. Comput. 26(4):1066–1099, [1997]), our fast SO(3) algorithm can be improved to give an algorithm of complexity O(B 3log 2 B), but at a cost in numerical reliability. Numerical and empirical results are presented establishing the empirical stability of the basic algorithm. Examples of applications are presented as well.

Estimating Granger causality from Fourier and wavelet transforms of time series data

Abstract: Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.

Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications.

Abstract: A computational technique for solving the MP2 equations for periodic systems using a local-correlation approach and implemented in the CRYSCOR code is presented. The Hartree-Fock solution provided by the CRYSTAL program is used as a reference. The motivations for the implementation of the new code are discussed, and the techniques adopted are briefly recalled. With respect to the original formulation (Pisani et al., J Chem Phys 2005, 122, 094113), many new features have been introduced in CRYSCOR to improve its efficiency and robustness. In particular, an adaptation of the density fitting scheme to translationally periodic systems is described, based on Fourier transformation techniques. Three examples of application are provided, concerning the CO(2) crystal, proton transfer in ice XI, and the adsorption of methane on MgO (001). The results obtained with the periodic LMP2 method for these systems appear more reliable than the ones obtained using density functional theory.

Color Image Watermarking Using Multidimensional Fourier Transforms

Abstract: This paper presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the frequency domain that is consistent with our human visual system. Watermark casting is performed by estimating the just-noticeable distortion of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image into the CIE chromaticity coordinates while the achromatic content is encoded as CIE tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using the spatiochromatic discrete Fourier transform. It first encodes and as complex values, followed by a single discrete Fourier transform. The most interesting characteristic of the scheme is the possibility of performing watermarking in the frequency domain of chromatic components. The second method encodes the components of color images and watermarks are embedded as vectors in the frequency domain of the channels by using the quaternion Fourier transform. Robustness is achieved by embedding a watermark in the coefficient with positive frequency, which spreads it to all color components in the spatial domain and invisibility is satisfied by modifying the coefficient with negative frequency, such that the combined effects of the two are insensitive to human eyes. Experimental results demonstrate that the two proposed algorithms perform better than two existing algorithms - ac- and discrete cosine transform-based schemes.

Terahertz imaging with compressed sensing and phase retrieval

Abstract: We describe a novel, high-speed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64 x 64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels, which defines the image in the Fourier plane, and observe improved reconstruction quality when we apply phase correction. For our chosen image, only about 12% of the pixels are required for reassembling the image. In combination with phase retrieval, our system has the capability to reconstruct images with only a small subset of Fourier amplitude measurements and thus has potential application in THz imaging with cw sources.

Pricing discretely monitored barrier options and defaultable bonds in lévy process models: a fast hilbert transform approach

Abstract: This paper presents a novel method to price discretely monitored single- and double-barrier options in Levy process-based models. The method involves a sequential evaluation of Hilbert transforms of the product of the Fourier transform of the value function at the previous barrier monitoring date and the characteristic function of the (Esscher transformed) Levy process. A discrete approximation with exponentially decaying errors is developed based on the Whittaker cardinal series (Sinc expansion) in Hardy spaces of functions analytic in a strip. An efficient computational algorithm is developed based on the fast Hilbert transform that, in turn, relies on the FFT-based Toeplitz matrix–vector multiplication. Our method also provides a natural framework for credit risk applications, where the firm value follows an exponential Levy process and default occurs at the first time the firm value is below the default barrier on one of a discrete set of monitoring dates.

Diffusion and mixing in fluid flow

Abstract: We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time, provided that the flow amplitude is large enough. The necessary and suficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow. In particular, we find that weakly mixing flows always enhance dissipation in this sense. The proofs are based on a general criterion for the decay of the semigroup generated by an operator of the form G + iAL with a negative unbounded self-adjoint operator G, a self-adjoint operator L, and parameter A » 1. In particular, they employ the RAGE theorem describing evolution of a quantum state belonging to the continuous spectral subspace of the hamiltonian (related to a classical theorem of Wiener on Fourier transforms of measures). Applications to quenching in reaction-diffusion equations are also considered.

High-efficiency rotating point spread functions.

Abstract: Rotating point spread functions (PSFs) present invariant features that continuously rotate with defocus and are important in diverse applications such as computational imaging and atom/particle trapping. However, their transfer function efficiency is typically very low. We generate highly efficient rotating PSFs by tailoring the range of invariant rotation to the specific application. The PSF design involves an optimization procedure that applies constraints in the Gauss-Laguerre modal plane, the spatial domain, and the Fourier domain. We observed over thirty times improvement in transfer function efficiency. Experiments with a phase-only spatial light modulator demonstrate the potential of high-efficiency rotating PSFs.

Massively parallel X-ray holography

Abstract: Advances in the development of free-electron lasers offer the realistic prospect of nanoscale imaging on the timescale of atomic motions. We identify X-ray Fourier-transform holography1,2,3 as a promising but, so far, inefficient scheme to do this. We show that a uniformly redundant array4 placed next to the sample, multiplies the efficiency of X-ray Fourier transform holography by more than three orders of magnitude, approaching that of a perfect lens, and provides holographic images with both amplitude- and phase-contrast information. The experiments reported here demonstrate this concept by imaging a nano-fabricated object at a synchrotron source, and a bacterial cell with a soft-X-ray free-electron laser, where illumination by a single 15-fs pulse was successfully used in producing the holographic image. As X-ray lasers move to shorter wavelengths we expect to obtain higher spatial resolution ultrafast movies of transient states of matter. X-ray Fourier transform holography using free-electron lasers has the potential to enable nanoscale imaging on the timescale of atomic motion. A technique that dramatically increases the efficiency of this technique could move us a step towards such imaging.

Development and Implementation of a Synchrophasor Estimator Capable of Measurements Under Dynamic Conditions

Abstract: The classical two-parameter Fourier algorithm for computing synchrophasors is appropriate when the underlying voltage and current waveforms are sinusoids with constant amplitude and phase angle and with a frequency equal to the assumed value. Synchrophasor measurements, however, are applied in power systems to track dynamic conditions where, by definition, currents and voltages, though resembling sine-waves, exhibit changes in their magnitudes and vectorial positions. This paper presents a novel algorithm for estimating synchrophasors under such dynamic conditions. In contrast to the classical Fourier algorithm, our model is a complex Taylor expansion, yielding several parameters in the model to be estimated. Four- and six-parameter models are presented corresponding to first and second order Taylor expansions. This paper derives a compensation method for canceling the error in the classical Fourier algorithm that arises under dynamic conditions, shows comparative simulation and test results and describes an efficient implementation. Application of the error cancellation method to other phasor algorithms and extending the technique to higher order Taylor expansions, are discussed. Implementation of synchrophasor measurements on protection and control intelligent electronic devices (IEDs) is discussed, and solutions are presented that allow for secure integration.

Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper.

Abstract: We report two-color two-dimensional Fourier transform electronic spectroscopy obtained using an acousto-optic pulse-shaper in a pump-probe geometry. The two-color setup will facilitate the study of energy transfer between electronic transitions that are widely separated in energy. We demonstrate the method at visible wavelengths on the laser dye LDS750 in acetonitrile. We discuss phase-cycling and polarization schemes to optimize the signal-to-noise ratio in the pump-probe geometry. We also demonstrate that phase-cycling can be used to separate rephasing and nonrephasing signal components.

On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations

Abstract: We improve and extend some known regularity criterion of the weak solution for the 3D viscous Magneto-hydrodynamics equations by means of the Fourier localization technique and Bony’s para-product decomposition.

Windowed Fourier transform for fringe pattern analysis: theoretical analyses.

Abstract: A windowed Fourier ridges (WFR) algorithm and a windowed Fourier filtering (WFF) algorithm have been proposed for fringe pattern analysis and have been demonstrated to be versatile and effective. Theoretical analyses of their performances are of interest. Local frequency and phase extraction errors by the WFR and WFF algorithms are analyzed in this paper. Effectiveness of the WFR and WFF algorithms will thus be theoretically proven. Consider four phase-shifted fringe patterns with local quadric phase [c(20)=c(02)=0.005 rad/(pixel)(2)], and assume that the noise in these fringe patterns have mean values of zero and standard deviations the same as the fringe amplitude. If the phase is directly obtained using the four-step phase-shifting algorithm, the phase error has a mean of zero and a standard deviation of 0.7 rad. However, when using the WFR algorithm with a window size of sigma(x)=sigma(y)=10 pixels, the local frequency extraction error has a mean of zero and a standard deviation of less than 0.01 rad/pixel and the phase extraction error in the WFR algorithm has a mean of zero and a standard deviation of about 0.02 rad. When using the WFF algorithm with the same window size, the phase extraction error has a mean of zero and a standard deviation of less than 0.04 rad and the local frequency extraction error also has a mean of zero and a standard deviation of less than 0.01 rad/pixel. Thus, an unbiased estimation with very low standard deviation is achievable for local frequencies and phase distributions through windowed Fourier transforms. Algorithms applied to different fringe patterns, different noise models, and different dimensions are discussed. The theoretical analyses are verified by numerical simulations.

Digital Computation of Linear Canonical Transforms

Abstract: We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ~ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.

High Frequency Resolution Techniques for Rotor Fault Detection of Induction Machines

Abstract: Motor current signature analysis (MCSA) is the reference method for the diagnosis of medium-large machines in industrial applications. However, MCSA is still an open research topic, as some signatures may be created by different phenomena, wherein it may become sensitive to load and inertia variations, and with respect to an oscillating load torque, although suitable data normalization can be applied. Recently, the topic of diagnostic techniques for drives and low to medium size machines is becoming attractive, as the procedure can be embedded in the drive at no additional thanks to a dedicated firmware, provided that a suitable computational cost is available. In this paper, statistical time-domain techniques are used to track grid frequency and machine slip. In this way, either a lower computational cost or a higher accuracy than traditional discrete Fourier transform techniques can be obtained. Then, the knowledge of both grid frequency and machine slip is used to tune the parameters of the zoom fast Fourier transform algorithm that either increases the frequency resolution, keeping constant the computational cost, or reduces the computational cost, keeping constant the frequency resolution. The proposed technique is validated for rotor faults.

Fourier transform light scattering of inhomogeneous and dynamic structures.

Abstract: Fourier transform light scattering (FTLS) is a novel experimental approach that combines optical microscopy, holography, and light scattering for studying inhomogeneous and dynamic media. In FTLS the optical phase and amplitude of a coherent image field are quantified and propagated numerically to the scattering plane. Because it detects all the scattered angles (spatial frequencies) simultaneously in each point of the image, FTLS can be regarded as the spatial equivalent of Fourier transform infrared spectroscopy, where all the temporal frequencies are detected at each moment in time.

Fourier Transform White-Light Interferometry for the Measurement of Fiber-Optic Extrinsic Fabry–PÉrot Interferometric Sensors

Abstract: A Fourier transform white-light interferometry for the absolute measurement of fiber-optic extrinsic Fabry-Perot interferometric sensors is presented The continuous test shows the variation is plusmn03 mum when measuring a cavity length of 2300 mum By combining with an average calculation, the variation of the measured results is only plusmn10 nm

Sampling and Sampling Rate Conversion of Band Limited Signals in the Fractional Fourier Transform Domain

Abstract: The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.

Making Sense of the Legendre Transform

Abstract: The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.