Estimation of the complex frequency of a harmonic signal based on a linear least squares method

In this study, we propose a simple linear least squares estimation method(LLS) based on a Fourier transform to estimate the complex frequency of a harmonic signal. We first use a synthetically-generated noisy time series to validate the accuracy and effectiveness of LLS by comparing it with the commonly used linear autoregressive method(AR). For an input frequency of 0.5 m Hz, the calculated deviations from the theoretical value were 0.004‰and 0.008‰ for the LLS and AR methods respectively; and for an input 5 10 6attenuation,the calculated deviations for the LLS and AR methods were 2.4% and 1.6%. Though the theory of the AR method is more complex than that of LLS, the results show LLS is a useful alternative method. Finally, we use LLS to estimate the complex frequencies of the five singlets of the0S2 mode of the Earth’s free oscillation. Not only are the results consistent with previous studies, the method has high estimation precisions, which may prove helpful in determining constraints on the Earth’s interior structures.

Negative Refraction at a Lossy Interface and a Bold Hypothesis via Complex Frequency

We investigate the negative refraction effect at a planar interface of a highly absorptive material,where the direct experimental verification is difficult because of the loss-induced skin depth effect. An apparent contradiction occurs when we try to determine the group velocity direction by the method of equifrequency contours(EFCs) in detail. This contradiction forbids any physical solution to be found for negative refraction.We conclude that this paradox is mainly caused by the definition of complex wavevector ■which is conventionally adopted in the case of complex permittivity. The complex wavevector may result in ambiguously defined optical path, which limits the application of the classical Snell’s law. We propose a bold suggestion that the complex wavevector■ should be replaced by a complex frequency■ . Therefore, the optical path can always be defined as real. The proposed hypothesis is capable of resolving the contradiction about the loss-induced negative refraction,and the obtained theoretical prediction fits well with the reported experimental results.

Third-order active-RC complex filter with automatic frequency tuning for ZigBee transceiver applications

A 3rd-order Butterworth active-RC complex band-pass filter was presented for Zig Bee(IEEE802.15.4) transceiver applications. The filter adopted cascaded complex pole stages to realize the 3 MHz bandwidth with a centre frequency of 2 MHz which was required by the Zig Bee transceiver applications. An automatic frequency tuning scheme was also designed to accommodate the performance deterioration due to the process, voltage and temperature(PVT) variations. The whole filter is implemented in a 0.18 μm standard process and occupies an area of 1.3 mm×0.6 mm. The current dissipation is 1.2 m A from a 1.8 V single power supply. Measurement results show that the image rejection ratio(IRR) of the filter is 24.1 d B with a pass-band ripple less than 0.3 d B. The adjacent channel rejection is 29.8 d B@7 MHz and alternate channel rejection 47.5 d B@12 MHz, respectively.

Complex Mode Frequency Iteration Method for Flutter Analysis of 2-DOF Systems

For a vibration system with 2 DOF of bend and torsion, its critical flutter wind speed can be calculated by using complex mode frequency iteration (CMFI) method based on MatLab 5.2, the results of which are in agree with those acquired by wind tunnel test. Not only critical flutter wind speed, but also vibration characteristic of a system under different wind speeds can be determined. CMFI method is suitable for both of separated flow torsional flutter and classic coupling flutter analysis, which is presented by flutter analysis of an ideal thin plate and a bluff bridge deck. Furthermore, it is proved through the investigation of the relationship between flutter derivatives and its critical flutter wind speed that coupling aerodynamic derivatives are necessary for classic coupling flutter to occur.]

Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.

Higher order implicit CNDG-PML algorithm for left-handed materials

By incorporating the higher order concept,the piecewise linear recursive convolution(PLRC)method and CrankNicolson Douglas-Gunn(CNDG)algorithm,the unconditionally stable complex frequency shifted nearly perfectly matched layer(CFS-NPML)is proposed to terminate the left-handed material(LHM)domain.The proposed scheme takes advantages of CFSNPML formulation,the higher order concept PLRC method and the unconditionally stable CNDG algorithm in terms of absorbing performance,computational efficiency,calculation accuracy and convenient implementation.A numerical example is carried out to demonstrate the effectiveness and efficiency of the proposed scheme.The results indicate that the proposed scheme can not only have considerable absorbing performance but also maintain the unconditional stability of the algorithm with the enlargement of time steps.

An investigation into natural vibrations of fluid-structure interaction systems subject to Sommerfeld radiation condition

A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.

Vibration of axially moving beam supported by viscoelastic foundation

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

Finite Element Method for Transient Electric Field by Using Indirect Laplace Transform with High Accuracy

This paper focuses on the finite element method in the complex frequency domain(CFD-FEM)for the transient electric field.First,the initial value and boundary value problem of the transient electric field under the electroquasistatic field in the complex frequency domain is given.In addition,the finite element equation and the constrained electric field equation on the boundary are derived.Secondly,the indirect algorithm of the numerical inverse Laplace transform is introduced.Based on it,the calculation procedures of the CFD-FEM are illustrated in detail.Thirdly,the step response,zero-state response under the positive periodic square waveform(PPSW)voltage,and the zero-input response by the CFD-FEM with direct algorithm and indirect algorithm are compared.Finally,the reason for the numerical oscillations of the zero-state response under the PPSW voltage is analyzed,and the method to reduce oscillations is proposed.The results show that the numerical accuracy of the indirect algorithm of the CFD-FEM is more than an order of magnitude higher than that of the direct algorithm when calculating the step response of the transient electric field.The proposed method can significantly reduce the numerical oscillations of the zero-state response under the PPSW voltage.The proposed method is helpful for the calculation of the transient electric field,especially in the case of frequency-dependent parameters.

Generalized system function analysis of resonant behavior of electromagnetic open systems

Abstract The generalized system function, H（s）, directly associated with the radiated or scattered fields is presented to effectively analyze the special resonant behavior of electromagnetic open systems in this paper, which is adaptively constructed by using the model-based parameter estimation （MBPE） technique in the complex frequency domain. By analyzing the characteristics of complex zeros, poles and residues of H（s） in a finite operational frequency band, we can effectively determine resonant frequencies and resonant intensity of electromagnetic open systems. It is known that an analysis of Q-factor of antenna and scattering systems has been an interesting and challenging problem. Based on H（s） and the complex frequency w theories, a complex frequency method for Q-factor of electromagnetic open systems is presented in this paper. Some examples of the practical antenna arrays are given to illustrate the applications and validity of the generalized system function theory proposed by this paper.