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We present a Fourier domain beamforming method for ultrafast pulse-echo imaging that significantly reduces the number of acquired samples. In its basic form, our proposed method combines the low-rate in-phase and quadrature sampling of the received analog radio frequency (RF) signals and the electronic receive focusing in the temporal Fourier domain. Using both synthetic and in vivo measurement data,...
The numerical inversion of the Laplace transform (NILT) is widely used in several engineer applications particularly in Electromagnetic Transients (EMT). Many works that use NILT were motivated by finding an easy, fast and accurate way to solve differential equations, in order to obtain a numerical solution. Based on the comparison between analytical results and NILT algorithms results, the effectiveness...
This paper proposes a PWM method reducing harmonics of two interleaved converters at twice the switching frequency region. If harmonics at twice the switching frequency region can be reduced by the PWM method, the size of filter interfacing the grid and converter would be reduced. Based on Fourier series of phase voltage in every switching period, offset voltage for PWM minimizing harmonics at twice...
The approximation of linear time-invariant (LTI) systems by sampling series is a central task of signal processing. For the Paley-Wiener space PW1π of bandlimited signals with absolutely integrable Fourier transform, it is known that there exist signals and stable LTI systems such that the canonical approximation process diverges. In this paper we analyze the structure of the sets of signals and systems...
Acquisition and perfect reconstruction of finite rate of innovation (FRI) signals was proposed first by Vetterli, Marziliano, and Blu [1]. To the best of our knowledge, the stability of their reconstruction procedure in the presence of scalar quantizers has not been addressed in the literature. For periodic stream of Dirac FRI signal, which is an important subclass of FRI signals, the stability of...
The components of the radiation patterns can be spanned with trigonometric polynomials in Multilevel Fast Multipole Algorithm (MLFMA) allowing development of simple global interpolators with exceptional accuracy control. In this article the basic properties of these functions are studied in one variable case. It is shown how the orthogonality of the basis functions can be utilized to develop simple...
In the paper we consider a new method based on the neural network for finding the location of small holes in the domain, in which the coupled linear and nonlinear boundary value problems are defined. The linear and nonlinear components are connected by the transmission conditions on the interface boundary. We use an artificial neural network, which calculates the locations of hole in the linear component...
During the last few decades, an extensive research effort has been aimed at studying and developing novel structures based on the photonic crystals composed of the multilayered arrays of periodically distributed circular rods. A photonic crystal with a complete bandgap has been used to localize electromagnetic waves to specific arrays and to guide the propagation of electromagnetic waves along certain...
A method to compute patterns of arbitrary planar antenna arrays based on DFT (Discrete Fourier Transform) is proposed. By complex Fourier series expansion, irregular arrays are approximated to regular arrays. And array patterns are obtained by applying DFT. Examples are provided to illustrate the proposed method. A comparison between the proposed method and the series summation method is performed...
Distance information is useful for satellite constellation. Evaluating the accuracy of spread spectrum receiver under finite bandwidth is still hard and few researches focus on that. In this paper, we build the signal model of DSSS signal under finite bandwidth, and then derive the mathematic form of error function. Furthermore, we propose the error factor, which is decided by bandwidth and early-to-late...
While nonlinear filtering for circular quantities is closely related to nonlinear filtering on linear domains, the underlying manifold enables the development of novel filters that take advantage of the boundedness of the domain. Previously, we introduced Fourier filters that approximate the density or its square root using Fourier series. For these filters, we proposed filter steps for arbitrary...
Differential equations are at the heart of physics and much of chemistry. In this paper, differential equations of convective-radiative longitudinal fins with convex and exponential profiles have been solved approximately using a Fourier-based optimization approach. Using the concepts of mathematics, Fourier series expansion, and metaheuristics, ordinary differential equations (ODEs) can be modeled...
We have proposed a new method for the scattering of electromagnetic waves by inhomogeneous dielectric gratings loaded with parallel perfectly conducting strips using the combination of improved Fourier series expansion method and point matching method. Numerical results are given for the transmitted scattered characteristics for TE and TM cases.
This paper presents a low harmonic 12 pulse rectifier. Then in order to investigate the influence of leakage inductance on 12 pulse rectifier. A set of improved switching function method is proposed. To obtain the mechanism that input current harmonics can be suppressed by circulating current of DC side, this paper analyzes the relationship between input current, output current and circulating current...
Real-time sampling and feedback can effectively reduce the sampling delay and improve the robustness of the active damping control for grid-connected LCL-filtered inverter. However, the practicability of this approach would be limited by the aliasing problem of sampling. In order to solve the aliasing problem, a systematic analysis is done to figure out the relation between the sampling instant of...
Time-Modulated Arrays (TMAs) perform angular diversity through the adaptive beamforming of their harmonic patterns with the advantage of employing a single Radio Frequency (RF) front-end. Rectangular pulses typically used in TMAs are not the best ones to efficiently distribute the spectral energy among the harmonics exploited. We propose a family of pulses, the so-called Sum of Weighted Cosines (SWC),...
The paper presents the study of a process's calculation in circuits with incommensurable frequencies. In such circuits the analysis of processes is realized by the use of an additional independent variable. Definitions of RMS currents, voltages and active power are introduced on the base of double integrals. Calculations of an active power in circuits with two independent voltage sources and a single-phase...
Usefulness of a bipolar pulse-frequency modulation (PFM) for DC-AC power converters with transformers are shown. The signal spectrum analyzing on the basis a double Fourier series are proposed. A separation of the bipolar PFM signal on two unipolar signals is developed. A time transform for the dependency of the bipolar PFM and a pulse-width modulation (PWM) is proposed. The effectiveness of the bipolar...
The synthesis of type A, B, and C pulse forming networks (PFNs) is relatively straightforward with Cauer and partial-fraction (Foster) expansion methods of the driving-point impedance or admittance functions. Analytical derivations of type D and E PFNs are much more difficult due to the necessity of calculating the negative inductances of the type D network. Type E networks are preferred in practice...
Pulse width modulation is a widely used technique for both DC to DC and DC to AC voltage conversion, with most modern-day DC and AC drives control systems exploiting this method. This paper presents a simple and versatile time domain method to determine the spectrum of a pulse width modulated converter output voltage for an arbitrary modulation signal waveform, an arbitrary number of output voltage...
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