In this paper, we propose a new technique for the transient scattering problem of periodically arrayed dispersion media for the TE case by using a combination of the Fourier series expansion method (FSEM) and the fast inversion Laplace transform (FILT) method, and analyze the pulse response for various widths of the dispersion media. As a result, we clarified the influence of the dispersion media with an air region on the resulting waveform.

The nth partial sums of a classical Fourier series have large oscillations near the jump discontinuities. This behaviour is the well-known Gibbs phenomenon. Recently, the inverse polynomial reconstruction method (IPRM) has been successfully implemented to reconstruct piecewise smooth functions by reducing the effects of the Gibbs phenomenon for Fourier series. This paper addresses the 2-D fractional Fourier series (FrFS) using the same approach used with the 1-D fractional Fourier series and finds that the Gibbs phenomenon will be observed in 1-D and 2-D fractional Fourier series expansions for functions at a jump discontinuity. The existing IPRM for resolution of the Gibbs phenomenon for 1-D and 2-D FrFS appears to be the same as that used for Fourier series. The proof of convergence provides theoretical basis for both 1-D and 2-D IPRM to remove Gibbs phenomenon. Several numerical examples are investigated. The results indicate that the IPRM method completely eliminates the Gibbs phenomenon and gives exact reconstruction results.

The accuracy of non-rigid 3D face recognition is highly influenced by the capability to model the expression deformations. Given a training set of non-neutral and neutral 3D face scan pairs from the same subject, a set of Fourier series coefficients for each face scan is reconstructed. The residues on each frequency of the Fourier series between the finely aligned pairs contain the expression deformation patterns and PCA is applied to learn these patterns. The proposed expression deformation model is then built by the eigenvectors with top eigenvalues from PCA. Recognition experiments are conducted on a 3D face database that features a rich set of facial expression deformations, and experimental results demonstrate the feasibility and merits of the proposed model.

In this paper, we apply an improved method for the guiding problem of dielectric waveguide with arbitrary inhomogeneous media along the middle layer introduced the defect layers, and analyzed the propagation characteristics of dielectric waveguide composed of dielectric circular cylinders and the arbitrary inhomogeneous media in the middle layer by using a combination of the improved Fourier series expansion method and multilayer method. Numerical results are given for the propagation constants in the first stop band regions, and the distribution of energy flow for both TE0 and TM0 modes. The influence of permittivity and the shape variation of arbitrary inhomogeneous media are discussed in the first stop band regions.

In the paper, a technique of the numerical inversion of multidimensional Laplace transforms (nD NILT), based on a complex Fourier series approximation is elaborated in light of a possible ralative error achievable. The detailed error analysis shows a relationship between the numerical integration of a multifold Bromwich integral and a complex Fourier series approximation, and leads to a novel formula relating the limiting relative error to the nD NILT technique parameters.

This paper presents a formulation of two-dimensional photonic crystal waveguide devices formed by circular cylinders. The device structures are considered as cascade connections of straight waveguides. Decomposing the structure into layers of the cylinder arrays, the input/output properties of the devices are obtained using an analysis method of multilayer structure. We introduce periodic boundary conditions in the direction perpendicular to the wave propagation, and the Floquet-modes of each layer are calculated by the Fourier series expansion method with the help of the recursive transition-matrix algorithm. Then, the input/output properties of the devices are obtained by recursive calculation of scattering matrix with each layer. The presented formulation is validated by numerical experiments by comparing with the previous works.

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.

In this paper, a fiber with two inhomogeneous sector holes around the core is proposed, and propagation characteristics of polarization maintaining region and single-polarization region are numerically analyzed by circular Fourier expansion method. In each case of the single-polarization region and the polarization maintaining region, a fiber is designed so as to satisfy the zero total dispersion at wavelength of 1.55 µm. Then, the single-polarization bandwidth for the single-polarization region and the modal birefringence for the polarization maintaining region are examined as the specific characteristics in each region. In addition, the power concentrating into the core region and distributions of Poynting vector is also discussed.

In digital transmission and storage systems, sequences must have attributes that comply with the physical characteristics of the channel. These channel constraints can often be satisfied through constrained sequence coding techniques which avoid use of sequences that violate the given channel constraints. In the design of a constrained code, it is usually helpful to consider the PSD of the encoded sequence in order to ensure that PSD requirements are met, and to obtain an indication of bandwidth, response at dc, average power peaks, and other spectral characteristics of interest. In this paper, we introduce an approach for the construction of finite-state sequential machine (FSSM) modeled encoders to satisfy spectral requirements. This approach involves construction of either a Mealy or a Moore FSSM to represent the encoder, and evaluation of the state transition probabilities and codeword values such that the PSD of the designed code meets a predefined spectral shape. Examples in this paper demonstrate the usefulness of this approach.

The propagation characteristics of the leaky TE mode in a two-dimensional photonic crystal waveguide is analyzed using the Fourier series expansion method combined with the Chew's perfectly matched layer (PML). The complex propagation constant and mode field profiles are numerically tested in detail. It is shown that the leakage phenomena can be well modeled by choosing the PML parameters in proper range.

In this paper, we propose a new technique for the scattering problems of multilayered inhomogeneous columnar dielectric gratings loaded rectangular dielectric constant both TM and TE waves using the combination of improved Fourier series expansion method, the multilayer method, and the eigenvalue matrix method. Numerical results are given for the power transmission coefficients in the parameters ε 3 /ε 0 , c/p, and b/d of rectangular cylinders to obtain the basic characteristic of the power transmission coefficients and reflection coefficients switching or frequency selective devices for both TM and TE waves. The influence of the incident angle and frequency of the transmitted power are also discussed in the connection with the propagation constant β in the free mode.

In this paper, we propose a new method for the electromagnetic fields with inhomogeneous media mixed a positive and negative regions by the combination of improved Fourier series expansion method using the extrapolation method which obtains the correct value of the eigenvalue and eigenvectors for the case of TM wave. Numerical results are given for the power reflection and transmission coefficient, the energy absorption, the electromagnetic fields, and the power flow in the inhomogeneous medium mixed the positive and negative regions including the case when the permittivity profiles touches zero for the TM wave. The results of our method are in good agreement with exact solution which is obtained the modified multilayer approximation method.

In this paper, we propose an on-line writer recognition method for Thai numeral. A handwriting process is characterized by a change of numeral's shape, which is represented by two features, a displacement of pen-point position and an area of triangle determined from the two adjacent points of pen-point position and the origin. First, the above two features are expanded into Fourier series. Secondly, in order to describe feature of handwriting, FIR (Finite impulse response) system having the above Fourier coefficients as input and output of the system is introduced. The impulse response of the FIR system is used as the feature of handwriting. Furthermore, K-L expansion of the obtained impulse response is used to recognize writer. Writer recognition experiments are performed by using 3,770 data collected by 54 Thai writers for one year. The average of Type I (false rejection) error rate and Type II (false acceptance) error rate were 2.16% and 1.12%, respectively.

Event-related are the kind of signals that are time-related to a given event. In this work, we will study the effect of bias and overlapping noise on Fourier linear combiner (FLC)-based filters, and its implication on filtering event-related signals. We found that the bias alters the weights behaviour, and therefore the filter output, and we discuss solutions to the problem of spectral overlap.

The blazing effects of dielectric grating consisting of two adjacent sinusoidally modulated layers which lead to the asymmetric profiles on a substrate are analyzed by using improved Fourier series expansion method. This method can be applied to the wide range of grating structure and gave high accurate results by comparing with those obtained by previous method. In this paper, the efficient blazing effects can be achieved by varying normalized distance (w/p) and the normalized thickness (d1/D), where D is kept fixed. The results are greater than those of trapezoidal profiles and triangular profiles. The influences of the second order of modulation index on the radiation efficiencies and normalized leakage factor are also discussed.

The propagation characteristics of dielectric waveguides with slanted grating structure are analyzed by using the combination of the improved Fourier series expansion method and the approximated multilayer method. The slanted grating region is appoximated by a structure with stratified thin modulated index layers. This method is effective to the guiding problems of the planar slanted grating, because the electromagnetic fields in each layer can be expressed by shifting the phase of the solution in the first layer. In this paper, numerical results are given for the grating with the rectangular and the sinusoidal profile for arbitrary slant angle. The radiation efficiencies for the grating with negative and positive slant angle are also discussed.

We introduce a procedure to determine the discrete Fourier spectra of the band-limited function from its irregularly distributed samples. The nonuniform data of the signal are represented by the non-orthogonal basis functions (non-harmonic Fourier functions) and discrete Fourier spectra of the signal. We construct a set of orthonormal basis functions from the above mentioned non-orthogonal basis functions using the Gram-Schmidt procedure. Based on the G-S procedure and the property of the orthogonalization, the spectral components of signal can be obtained by the conjugate transpose of orthonormal basis functions, their coefficients matrix and the nonuniform samples. Thus the desired signal can be obtained by the inverse Fourier transform of the determined discrete Fourier spectra. We apply this algorithm to reconstruct a band-limited low-pass and band-pass signal and show that our method provide more stable and better reconstruction than the matrix inversion method.

The relation between the radiation pattern and the dimension of the conducting box for a portable telephone is illustrated both theoretically and experimentally. The Galerkin-moment method using the Fourier series expansion for the surface current of the conducting box, which has a great advantage of having a high accuracy, is employed to obtain the radiation pattern. As an example of antennas, a quarter-wavelength monopole antenna having a sinusoidal current distribution is used. As a result, it is pointed out that the radiation pattern of a monopole antenna mounted on the box tends to tilt in a lower direction both in theory and in experiment as well. The relation between the radiation pattern and the location of the monopole antenna is also described. An asymmetrical, or distorted pattern is observed when the monopole antenna moves away from the center of the top plane.

The scattering of electromagnetic waves by a dielectric grating with planar slanted-fringe is analyzed using the improved Fourier series expansion method. In the analysis, the slanted grating region is divided into layers to make an assembly of stratified thin modulated index layers. This method can be applied to a wide range of periodic structures and is especially effective in the case of planar slanted grating, because the electromagnetic fields in the each layer can easily be obtained by shifting the solution in the first layer. In this paper, the numerical results are given for grating with rectangular and sinusoidal dielectric profiles, and for TM and TE cases of arbitrary incident angle. The diffraction efficiencies obtained by the presented method are compared with the results by the coupled-wave approach; the influences of the slant angle on the diffraction efficiencies at the Wood's anomaly and at the coupling resonance frequency are also discussed.

In this paper, the characteristics of microstrip lines near the edge of dielectric substrate are analyzed by improving the rectangular boundary division method. The numerical results indicate the changes of the characteristics of a microstrip line when the strip conductor is closely located to the edge. When the distance the dielectric substrate edge to the strip conductor is less than the thickness of dielectric substrate, the effects of the edge on the line characteristics are no longer negligible. The numerical results in this paper show high computation accuracy without increasing computation time. Our improvement is effective for the analysis of the microstrip lines both for the narrow strip conductor and the strip conductor close to the edge. The relative errors between the numerical results and the measured values are less than 1.2%.