Fast algorithm to calculate fourier transform

Aims: We show the use of principal component analysis (PCA) and Fourier decomposition (FD) method as tools for variable star diagnostics and compare their relative performance in studying the changes in the light curve structures of pulsating Cepheids and in the classification of variable stars. Methods: We have calculated the Fourier parameters of 17,606 light curves of a variety of variables, e.g., RR Lyraes, Cepheids, Mira Variables and extrinsic variables for our analysis. We have also performed PCA on the same database of light curves. The inputs to the PCA are the 100 values of the magnitudes for each of these 17,606 light curves in the database interpolated between phase 0 to 1. Unlike some previous studies, Fourier coefficients are not used as input to the PCA. Results: We show that in general, the first few principal components (PCs) are enough to reconstruct the original light curves compared to FD method where 2 to 3 times more number of parameters are required to satisfactorily reconstruct the light curves. The computation of required number of Fourier parameters on the average needs 20 times more CPU time than the computation of required number of PCs. Therefore, PCA does have some advantage over the FD method in analysing the variable stars in a larger database. However in some cases, particularly in finding the resonances in Fundamental mode (FU) Cepheids, the PCA results show no distinct advantages over the FD method. We also demonstrate that the PCA technique can be used to classify variables into different variability classes in an automated, unsupervised way, a feature that has immense potential for larger databases of the future.

An investigation of the frequency and amplitude of sampled signals using Fourier series A sinusoid is sampled above and below the Nyquist rate and using a simple Fourier series technique, the impulse response is reconstructed to show the frequency and amplitude of the resulting sideband signals. From this information the frequency spectrum of bandwide signals, when sampled, is developed. Recovery of signals above and under the Nyquist rate is then investigated.

Quantum extreme learning machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate—the quantum reservoir—and the efficient post-measurement training via linear regression. Here, we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. In particular, our result on the reservoir-induced concentration strongly indicates that quantum reservoirs drawn from a highly random ensemble make QELM models unscalable. Our analysis elucidates the potential and fundamental limitations of QELMs and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

The OGLE database is revisited to investigate in more detail the properties of the Fourier parameters. Methodological improvements led us to identify a clear separation among High-Amplitude δ Scuti (HADS), RRc and RRab stars. The bimodal distribution of the R21 parameter in HADS stars is explained as a contamination effect from RRc stars: there is evidence that all stars with d are RRc variables. The previously claimed existence of a subclass of unusual HADS is demonstrated to be a spurious result. Candidate overtone pulsators are found among HADS and RRc variables. The properties of the Fourier parameters are discussed as a function of the physical conditions in the stars involved. Among the field RRab stars we detected different light-curve groups producing distinct "tails" in the Fourier plots for d; evolutionary phases or the combination of different physical conditions (not only metallicity) are suggested to explain this separation, observed also in the cluster RRab stars. The stellar parameters of RRc stars in a given globular cluster show different tendencies than those of RRc stars from different clusters.

A simulation approach to the comparative analysis of various job scheduling methods

Efficient large deflection analysis of rectangular orthotropic plates by direct energy minimisation

Dual laterolog (DLL) makes use of a galvanic conduction principle to focus electrical currents into rock formations, thereby minimizing shoulder and borehole effects in the measurement of formation resistivity. The tool includes two separate focusing systems: deep-sensing (LLd) and shallow-sensing modes (LLs). Laterolog current-focusing systems were designed for operation primarily in vertical boreholes penetrating horizontal layers; only recently their design has been revised for operation in deviated wells in the presence of electrical anisotropy. We simulated three-dimensional (3D) DLL measurements in dipping, invaded, and electrically anisotropic formations and appraised the corresponding effects on apparent resistivity logs. Simulations were performed by combining the use of a Fourier-series expansion in a nonorthogonal system of coordinates with an existing 2D goal-oriented, higher-order, and self-adaptive finite-element method. This numerical algorithm yields accurate solutions in limited CPU time because only a few Fourier modes are needed to simulate practical applications. For the calculation of focused currents, we introduced an embedded postprocessing method that incorporates a synthetic focusing principle to compute current intensities at each iterative step of optimal mesh refinements. Our numerical method accurately simulates 3D DLL measurements in rock formations that exhibit extreme contrasts of electrical resistivity. Simulations indicate that LLs resistivity logs are more sensitive to both invaded and anisotropic layers than LLd resistivity logs. In deviated wells, shoulder-bed effects on apparent resistivity logs increase with an increase of dip angle, and are emphasized across thin conductive layers. Electrical anisotropy effects on apparent resistivity logs increase substantially with dip angle.

In this paper, an algorithm for band-limited extrapolation is presented. This uses Shannon's sampling theorem and Fourier series. Error analysis is given by proof. The convergence rate is much faster than that of the Papoulis-Gerchberg algorithm. The procedure of the fast convergence algorithm is described in detail. The result is demonstrated by numerical examples.

In this paper, we propose a new class of discontinuous orthogonal system called Walsh-U system, which is composed of piecewise polynomials of degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> in Hilbert space <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{2}[0, 1]$</tex-math></inline-formula> . The Walsh-U system generalizes the Walsh system from piecewise constant to piecewise polynomials, which is capable of representing discontinuous signals. Besides, the basis functions of the Walsh-U system not only possess a more concise construction, but also have stronger sparse representation capabilities than the U-system. In the construction of the Walsh-U system, the Legendre polynomials are adopted as the generators at first, and then a series of basis functions are produced through the generators and basic operations of scaling and replication. These basis functions are formed into different groups based on the generation order. Furthermore, a fast algorithm for the Walsh-U system is designed in this paper. The experimental results demonstrate that when compared with Fourier series, Walsh functions, wavelet functions, and U-system, the Walsh-U system has fast convergence and high approximation precision in analog signal reconstruction and denoising. It is verified that the fast algorithm for the Walsh-U system can effectively improve the computation speed for discontinuous signals.

At passive sounding the sources of observable radiation are often distributed casually. In this case the intensity of radiation is main information parameter for the decision of an inverse problem. To reconstruction 2D distribution of own radiation sources density on the basis of angular distribution registration of received radiation intensity the decomposition of known and unknown functions in Fourier series on circular harmonics is applied. In case of poor absorption the problem is reduced to equation of Abel type with Chebyshev polynomials in its kernel. New method is offered, which is based on exponential variable replacement. In this case the initial equation is resulted to the convolution equation that admit the decision by use fast algorithms. Efficiency and stability of the decision have been proved by results of initiation modeling. Opportunity of use of the decision for diagnostics of atmosphere radiating pollution and forest fire moving is shown.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction [Formula: see text]. We prove that the system is locally null-controllable in any positive time, by means of a control supported within an arbitrary open and non-empty subset. We proceed by a linear test and duality, but quickly find that the linearized system is not symmetric and the adjoint has a dynamic coupling between the two states through the (fixed) boundary. Hence, motivated by a Fourier decomposition with respect to [Formula: see text], we consider a family of one-dimensional systems and prove observability results which are uniform with respect to the Fourier frequency parameter. The latter results are also novel, as we compute the full spectrum of the underlying operator for the nonzero Fourier modes. The zeroth mode system, on the other hand, is seen as a controllability problem for the linear heat equation with a finite-dimensional constraint. The complete observability of the adjoint is derived by using a Lebeau–Robbiano strategy, and the local controllability of the nonlinear system is then shown by combining an adaptation of the source term method introduced in [Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid–structure interaction model, ESAIM Control Optim. Calc. Var. 19 (2013) 20–42] and a Banach fixed-point argument. Numerical experiments motivate several challenging open problems, foraying even beyond the specific setting we deal with herein.

Submerged breakwaters are a very common structural solution employed for shore erosion control. Predicting wave climate leeward the barriers is indeed the main task to the functional design of such structures; this because it rules the distribution of wave thrusts in the protected area that, in turn, governs hydrodynamic and morphodynamic processes. In this regard it should be noticed that the interaction between waves and submerged breakwaters is a strongly non-linear process. In fact, when water waves come across the structure, multiple-frequency harmonic wave components arise, generating a transmitted wave field very different from the incident one. The super-harmonics consist of phase-locked waves to the fundamental one plus free waves that travels with their own phase speed in the shadow zone. These components interact leading all kinematic and dynamic quantities to spatially fluctuate behind the structure. The aim of this work is to investigate the main characteristics of the non-linear interaction between waves and submerged barriers for conditions of both breaking and no-breaking waves over the structure crown. For this purpose a long series of laboratory experiments have been carried out at the small scale wave flume of the Hydraulic, Geotechnical and Environmental Engineering Department (DIGA) of University of Naples “Federico II”. Models of rubble-mound submerged breakwaters with different geometries and porosity have been employed under the action of regular waves with different height and period. The free surface elevation process has been acquired at several positions leeward of structure models. Experimental results clearly show that the wave shape in the sheltered area is non-permanent leading the profile asymmetry coefficients spatially fluctuate as well as the twice frequency Fourier modes. This behavior, due to the interaction between phase-locked waves and free waves, leads the variance profile (i.e. the spectrum area) to fluctuate in the same way making the definition itself of transmitted wave height quite uncertain. As a further result it has been noticed that higher harmonics transmitted rate reaches a maximum value when waves start breaking over the structure and then, with increasing of dissipation process, to be reduced lying in a saturation curve.

Theoretical and experimental kineto elastodynamic analysis of high speed linkage

THEORETICAL ASPECTS OF TORQUE RESPONSES IN SPUR GEARING DUE TO MESH STIFFNESS VARIATION

Two and three level VSC inverters are the building blocks of most of inverter applications necessitating the employment of appropriate switching techniques that result in harmonic free sinusoidal output. The paper presents the generalized method for harmonic elimination in two and three level voltage sourced converter. The technique used for suppression of selective low-ordered harmonics form the inverter's output voltage waveform is Selective harmonic elimination (SHE). The inverter's output voltage waveform is mathematically modeled using Fourier series that results in the system of nonlinear equations. The non-linear equations are solved for eliminating the specific low order harmonics. The main objective in calculating appropriate switching angle is to minimize the value of Total Harmonic Distortion (THD). To solve the system of non-linear equations numerical method Newton Raphson is applied and appropriate switching angles are calculated. The remaining uneliminated higher order harmonics are eliminated by connecting appropriate value of filter at the output stage of VSC inverter. The model of two level VSC is simulated in SimPowerSystem Matlab tool bar together with the algorithm of Newton Raphson technique. The time domain plot and frequency spectrum of inverter's output waveform is presented in the results section. The results of two and three level VSC inverters are analyzed and debated together with the comparative analysis on the basis of THD. Moreover, a comparison is presented on the basis of IEEE standard Std. 519 and EN 50160.