预条件共轭梯度法在辐射和散射问题中的应用

用矩量法求解一些辐射和散射问题 ,如线天线辐射和线状体散射等问题时 ,可以产生一个 Toeplitz线性方程组 ,采用预条件共轭梯度法 (PCG)与快速富里叶变换 (FFT)的结合方法 (PCGFFT)来求解该方程组 ,其中预条件器采用 T.Chan的优化循环预条件器。使用 PCGFFT算法 ,可有效地节省内存 ,提高了计算速度。为说明其有效性 ,将 PCGFFT算法与 CGFFT算法以及 Levinson递推算法进行了对比。     

Preconditioned conjugate gradient methods for solving electromagnetic problems

It is shown that appropriately chosen preconditioners can significantly improve the convergence rate of the conjugate gradient (CG) algorithm as applied to electromagnetic problems. Preconditioners are constructed for the problems of scattering from frequency selective surfaces and scattering from infinite cylinders.     

Interpolation using the fast Fourier transform

The fast Fourier transform (FFT) algorithm has had widespread influence in many areas of computation since its "rediscovery" by Cooley and Tukey [1]. An efficient and accurate method for interpolation of functions based on the FFT is presented. As an application, the generation of the characteristic polynomial in the "generalized eigenvalue problem" [2] is considered.     

Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems

An iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems, in an attempt to characterize the typical rate of convergence of that method. It is found that this rate depends on the cell density per wavelength used in the discretization, the presence of symmetries in the solution, and the degree to which mixed cell sizes are used in the models. Assuming cell densities used in the discretization are in the range of ten per linear wavelength, the iterative algorithm typically requiresN/4toN/2steps to converge to necessary accuracy, whereNis the order of the matrix under consideration.     

Speech spectrograms using the fast Fourier transform

An important aid in the analysis and display of speech is the sound spectrogram, which represents a time-frequency?intensity display of the short-time spectrum.1-3 With many modern speech facilities centering around small or medium-size computers, it is often useful to generate spectrograms digitally, online. The fast Fourier transform algorithm provides a mechanism for implementing this efficiently.     

Diffraction calculations using fast Fourier transform methods

By using a coordinate transformation based on Gaussian-beam theory, we can apply efficient fast Fourier transform (FFT) computational methods to diffraction problems involving spherically diverging or converging waves as well as to quasi-collimated beams of radiation.     

A fast Gaussian method for Fourier transform evaluation

A Gaussian method for fast evaluation of approximations to Fourier integral transforms is presented. This method is faster than the FFT for transforms of functions that require considerable computer time to compute. It is especially useful when transforms of high accuracy are needed.     

The fast Fourier transform

The fast Fourier transform (FFT), a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained. Examples and detailed procedures are provided to assist the reader in learning how to use the algorithm. The savings in computer time can be huge; for example, an N = 210-point transform can be computed with the FFT 100 times faster than with the use of a direct approach.     

Integer fast Fourier transform

A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2^N-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power     

Conjugate pair fast Fourier transform

A new algorithm for the fast computation of the discrete Fourier transform is introduced. The algorithm, called the conjugate pair FFT (CPFFT), is used to compute a length-2/sup n/ DFT. The number of multiplications and additions required by the CPFFT is less than that required by the SRFFT algorithm.<>     

Calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and FFT

The scattering problem of an axially uniform dielectric cylinder is formulated in terms of the electric field integral equation, where the cylinder is of general cross-sectional shape, inhomogeneity, and anisotropy, and the incident field is arbitrary. Using the pulse-function expansion and the point-matching technique, the integral equation is reduced to a system of simultaneous equations. Then, a published procedure for solving the system using the conjugate gradient method and the fast Fourier transform (FFT) is generalized to the case of oblique-incidence scattering.     

A scheme to analyze conducting plates of resonant size using theconjugate-gradient method and the fast Fourier transform

A scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate-gradient (CG) method and the fast Fourier transform (FFT) is presented in detail. The problems are analyzed by solving their corresponding electric-field integral equation. The procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields. These functions have been widely used in moment-method (MM) applications. The scheme is an efficient numerical tool, benefiting from the good convergence and low memory requirements of the CG and the low CPU time consumed in performing convolutions with the FFT. In comparison with the MM, the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude. Several results are presented and compared with analytical, numerical, or measured values that appear in the literature     

Analysis of arbitrary metallic surfaces conformed to a circularcylinder using the conjugate gradient-fast Fourier transform (CG-FFT)method

An efficient scheme for analyzing electrodynamic problems involving arbitrary metallic surfaces conformed to a circular cylinder, using the conjugate-gradient-fast-Fourier-transform (CG-FFT) method, is presented. The numerical method outlined is efficient in CPU time and minimizes the memory storage requirements. Several results are presented and compared with numerical or measured values that appear in the literature     

A bus-oriented multiprocessor fast Fourier transform

A bus-oriented multiprocessor architecture specialized for computation of the discrete Fourier transform (DFT) of a length N =2^M sequential data stream is developed. The architecture distributes computation and memory requirements evenly among the processors and allows flexibility in the number of processors and in the choice of a fast Fourier transform (FFT) algorithm. With three buses, the bus bandwidth equals the input data rate. A single time-multiplexed bus with a bandwidth of three times the input data rate can alternatively be used. The architecture requires processors that have identical hardware, which makes it more attractive than the cascade (pipeline) FFT for multiprocessor implementation     

ADC testing using interpolated fast Fourier transform (IFFT) technique

An ideal transfer characteristic of an analogue-to-digital converter (ADC) is simulated and an arbitrary nonlinearity error is introduced. A full-scale sine wave is also simulated and applied to ADC input. The interpolated fast Fourier transform (IFFT) technique is used to determine accurately fundamental and other harmonics in the output spectrum of the ADC. The signal-to-noise ratio and the effective number of bits (ENOB) are computed on the basis of FFT and IFFT for different resolutions of ADC and test conditions. The effects of rectangular and Hanning time window functions on the determination of frequency components are reported. The proposed method of dynamic testing of the ADC is useful for users as well as manufacturers.     

Cavity mode analysis using the Fourier transform method

A novel and economical computer iterative method for cavity mode calculations is developed. The method involves the formulation of the cavity field in the form of Fourier integrals and involves the use of the fast Fourier transform as a computation tool for obtaining numerical results.     

Solution of electromagnetic scattering problems using time domaintechniques

New method are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves     

用小波变换快速求解三维电磁散射问题

在三维电磁散射问题中,用小波变换对由Ｒａｏ面片生成的阻抗矩阵进行稀疏化和求逆,比较了两种小波变换对阻抗矩阵的稀疏效果,由此指出了三维散射问题与二维散射问题中小波变换选取有所不同。通过分析和算例,表明小波变换可以有效减少阻抗矩阵的求逆时间,这对于计算电大尺寸散射体的ＲＣＳ是很有益的。     

Precise expression relating the Fourier transform of a continuoussignal to the fast Fourier transform of signal samples

The fast Fourier transform (FFT) signature of a finite duration, constant frequency, time signal displays sidebands which are a sampling artifact. An analytical expression is derived which precisely predicts artifact behavior. Using this expression, a precise spectral estimate (PSE) is derived. It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series. Furthermore, PSE is capable of resolving frequency to a fraction of an FFT frequency resolution cell