The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
It is found that the GARCH (1,1) model has a good fitting effect on the time series by the statistical analysis of the logarithmic yield of the closing price of the Shanghai Composite Index. Therefore, this paper first uses the model GARCH (1,1) predicts the daily closing price of the Shanghai Composite Index, and then uses the Fourier series to correct the predicted residuals to obtain the final...
The aim of the paper is to calculate the maximum magnetic induction value of the transformer's core which provides a specified value of current distortion. To solve this problem, an experimental study was made on the dependence of the magnetic induction on Total Harmonic Distortion for current. The processing of the measurement results was carried out using Fourier series, harmonic analysis and interpolation...
We propose a robust method for estimating the orientation and displacement of an inertial measurement unit undergoing planar periodic motion. Such movements is a common approximation to human gait and running. We formulate the problem introducing a sparse vector of outlier errors and l1-regularization. The problem thus becomes robust to outliers in the data. The problem can be rewritten as a quadratic...
We describe a design for an “audio display”, a loudspeaker that employs the bending vibrations of a panel, such as flat-panel television screen or projection surface, to render localized sound sources anywhere on the surface of the panel. The method employs a two-dimensional Fourier series reconstruction of the desired panel spatial vibration profile, and an array of force actuators affixed to the...
This paper designs a boundary controller for a reaction-advection-diffusion equation on the cylindrical surface with input delay. We introduce a transport partial differential equation (PDE) to remove the input delay by transforming the time delay into a spatial travelling. Then the system with time delay turns to a cascade system composed of two PDEs without delay. For the cascade system, we design...
The k-Wave MATLAB toolbox is widely used to conduct medical ultrasound simulations. It uses a Fourier collocation method to numerically solve the governing model equations, and introduces sources by adding acoustic pressure at points on an orthogonal grid. This approach introduces two errors when sources don't exactly align with the grid. These are phase errors arising from shifting source points...
An elegant analytical method for the derivation of the non-linear mathematical model of classical Costas electric circuit with non-sinusoidal signal waveforms is presented. Resulting model is similar to classical phase-locked loop (PLL) with special waveform of the phase detector characteristic. Phase detector characteristic can be computed analytically using Fourier series representation. The method...
In the paper, some specific problems occurring in analysis of critically sampled signals and their reconstruction are considered. These are the problems which are mostly omitted in the literature of the subject because they can lead to ambiguous results. Because of this reason, their explanation is hard and thankless. Here, we show how to find and verify the general description of the resulting signal...
This paper investigates dynamic visual feedback position tracking of two kinds of two-wheeled vehicles with a camera or a target object for visual measurements. A problem formulation is first provided, where the dynamics of the camera vehicle is explicitly considered and the target vehicle velocity is expressed by a Fourier series expansion. Next, passivity-based tracking control structure is explained...
Induction motors are one of the most widely used electrical machines. Statistics of bearing failures of induction motors indicate, that they constitute more than 40% of induction motor damage. Therefore, bearing diagnosis is so important for trouble-free work of induction motors. The most common methods of bearing diagnosis are based on vibration signal analysis. The main disadvantage of those methods...
Scattering of an incident TM wave from multiple dielectric cylinders with arbitrary cross sections is elaborated. Parametrization of each cross section is assumed to be infinitely smooth, i.e. it is infinitely differentiable according to its argument. We suggest the super-algebraically convergent algorithm to solve both electric/magnetic field integral equations (EFIE/MFIE) by proper factorization...
The high-frequency asymptotic procedure developed for the diffraction by an elongated body is proved to reduce the initial problem to a mathematically correct boundary-value problem for the parabolic equation. The analogue of “time” η varies on an interval [−1,1]. The problem is considered in the class of functions with not too singular behavior near η = ±1 and the solution is understood in the frame...
Sampling theory is a fundamental area of study in harmonic analysis and signal and image processing. We look at the key role the Poisson Summation Formula plays in sampling, and show its connection to the Selberg Trace Formula. We discuss harmonic analysis in both Euclidean and non-Euclidean spaces, and then focus on the connection of the Poisson Summation Formula to the Selberg Trace Formula in non-Euclidean...
We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse the connection between the discrete solution spaces and demonstrate the numerical benefits. Finite element methods arise as a special case of periodised Box spline...
We present different sampling methods for the approximation of functions on the sphere. In this note we focus on Fourier methods on the sphere based on spherical harmonics and on the double Fourier sphere method. Further longitude-latitude transformation is combined with Fourier extension to allow the use of bi-periodic Fourier series on the sphere. Fourier extension with hermite interpolation is...
The output power variation in individual cylinders must be detected to suppress combustion variation. We thus developed a method to estimate the coefficient of variation of combustion (COV) and the crank angle position of peak combustion torque from mass-produced crank angle sensor signals, which have insufficient resolution of tooth pitch and tooth pitch variation caused by manufacturing error. In...
The approximation of stable linear time-invariant systems is a central task in many applications. Therefore, it is important to know if a given approximation process is stable and converges for all signals from the signal space or if it is unstable and diverges for certain signals. Further, in the case of divergence, it is interesting to know whether the set of signals with divergent approximation...
The Magnetic Particle Imaging (MPI) is an emerging medical imaging technology which attracted the interest of different research groups in the last years [14]. The technique of the MPI is based on the detection of a tracer which consists of superparamagnetic iron oxide nanoparticles through the superimposition of different magnetic fields.
The Haar orthogonal system had been constructed in 1909 [7] as an answer on the question by D. Hilbert: is there exist an orthogonal system on the segment [0,1] such that the Fourier series of any continuous function with respect to this system converges uniformly on [0,1] to this function? The Haar system has many applications in the theory of orthogonal series and applied mathematics (see [9], [11]...
Nowadays, millimeter-wave communication centered at the 60 GHz radio frequency band is increasingly the preferred technology for near-field communication since it provides transmission bandwidth that is several GHz wide. The IEEE 802.11ad standard has been developed for commercial wireless local area networks in the 60 GHz transmission environment. Receivers designed to process IEEE 802.11ad waveforms...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.