The inversion of covariance matrices by finite Fourier transforms (Corresp.)

A matrix series is derived that converges to the inverse of a covariance matrix. The members of the series are derived from a circular matrix that can be inverted by taking finite Fourier transforms. An example of the method is presented.     

Calculating Chebyshev shading coefficients via the discrete Fourier transform

A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms. The reduced accuracy required for intermediate calculations is retained. Additionally, the fast Fourier transform can be used giving computational savings.     

Fast two-dimensional Hartley transform

The fast Hartley transform algorithm introduced in 1984 offers an alternative to the fast Fourier transform, with the advantages of not requiring complex arithmetic or a sign change of i to distinguish inverse transformation from direct. A two-dimensional extension is described that speeds up Fourier transformation of real digital images.     

Numerical inversion of the Laplace transform

In the numerical evaluation of the inverse Laplace transform, the result is marred by Gibbs oscillations in the same way as the inverse complex Fourier transform. Attention is drawn to means by which the representation can be improved and the numerical work eased.     

Computationally efficient methods for analysis and synthesis ofreal signals using FFT and IFFT

The discrete Fourier transform (DFT) and the inverse discrete Fourier transform (IDFT) are used in a wide variety of signal processing applications. Even with the increased speed of modern processors, there is an ongoing need to further develop more efficient methods for computing DFT and IDFT, with a particular effort to reduce the number of complex multiplications. The properties of certain complex sequences are extraordinarily useful in the sense that they lead to data manipulation schemes that result in the sequences to which traditional but much shorter fast Fourier transform (FFT) algorithms may be applied. This is achieved by exploiting a certain regularity in the complex data. The index-reversed complex conjugate sequence and the mirror symmetric complex conjugate sequence were defined. A significant reduction in the number of complex computations is achieved if a sequence in either domain exhibits such symmetry     

Inverse Class-AB功率放大器线性度和效率分析

inverse Class—AB模式可以使功率放大器得到更好的性能，但是传统的教科书中并没有这种模式的理论分析因此有必要从理论上对inverse Class-AB模式进行分析。通过对输出波形傅里叶函数的研究可以得到最大输出电压摆幅以及计算最大功率。通过Volterra序列分析法以out—of-band抵消技术我们分析这种模式功率放大器的非线性。最后我们进行了大量的仿真以验证所提出的理论。     

用APRGA求解二维导体柱电磁逆散射

从电磁散射的积分方程出发，利用点匹配法和脉冲基函数求解电磁散射问题，以测量的散射场和计算的散射场的偏差程度为目标函数，将待优化变量设置为描述导体柱轮廓的形状函数的傅立叶展开式系数，Ai0，Ai1…AiN/2,Bi1,Bi2…BiN/2,k=1,2…k，通过参数自适应实数遗传算法（APRGA）对待优化变量进行优化，使目标函数达到最小值来对自由空间中导体柱族进行电磁成像，证实了APRGA比BRGA有更好的收敛性能和成像精度，更强的抗随机噪声干扰能力。     

非均匀介质薄筒的电磁逆散射

本文采用傅里叶级数展开的方法,处理截面为窄圆环的二维损耗介质体的电磁逆散射问题,根据介质体的散射场解析地表达出它的电参数。模拟计算得到满意的结果。     

THE INVERSE ELECTROMAGNETIC SCATTERING OF INHOMOGENEOUS DIELECTRIC THIN TUBES

By using the method of Fourier series expansion, the inverse electromagnetic scattering problemof a 2- dimensional lossy dielectric body, of which the cross section is a narrow annulus, is studied. Theanalytic expressions of the electric parameters of a dielectric body are given in terms of the outsidesca,ttering field, and the simulative results are satisfactory.     

A study of the fields associated with horizontal dipole sources in stripline circuits

In this paper, we formulate closed-form expressions for the fields excited by an x-directed dipole source in both homogeneously-filled and inhomogeneously-filled stripline structures. These expressions are obtained by first employing spectral domain techniques, which yields a spectral-domain Green's function that involves simple algebraic and trigonometric functions. Then we take the inverse two-dimensional Fourier transform of that expression and represent it as a Sommerfield-type integral in the space domain. This Sommerfield integral has a highly oscillatory and slowly convergent nature. Therefore, we analytically evaluate this Sommerfield integral by applying residue theory. Summing over the residues evaluated at the pole locations in the complex plane yields a rapidly computable modal series expansion that is free from any numerical integration. The special functions that occur in the modal series expansions are rapidly computable Bessel functions. This method greatly improves the computational efficiency as compared with numerical integration. The field study carried out in this paper will help to extend the capabilities of a recently developed full-wave layered interconnect simulator (UA-FWLIS).     

平顶高斯光束通过硬边光阑传输算法的改进

用傅里叶级数和复高斯函数的乘积对硬边光阑的窗口函数进一步拟合,对平顶高斯光束通过硬边光阑光学系统的模拟算法作了改进,并给出了近似解析传输公式.对直接积分Collins公式和使用Wen方法的数值计算结果作了比较.研究表明,只要傅里叶级数项数不少于30,改进后的算法比直接用复高斯函数展开具有更高的计算精度.     

咀嚼过程人脸颊外形动态变化的光学三维测量

通过CCD摄像机快速获取由罗奇(Rochi)光栅投影到处于动态变化过程中人脸表面上的一系列变形条纹,经过傅立叶变换、频谱滤波、逆傅立叶变换及相位展开等处理后得到重建的一系列脸部颊面面形,再现处于咀嚼过程中的人脸颊部动态变化过程。     

A comparative review of real and complex Fourier-related transforms

Major continuous-time, discrete-time, and discrete Fourier-related transforms as well as Fourier-related series are discussed both with real and complex kernels. The complex Fourier transforms, Fourier series, cosine, sine, Hartley, Mellin, Laplace transforms, and z-transforms are covered on a comparative basis. Generalizations of the Fourier transform kernel lead to a number of novel transforms, in particular, special discrete cosine, discrete sine, and real discrete Fourier transforms, which have already found use in a number of applications. The fast algorithms for the real discrete Fourier transform provide a unified approach for the optimal fast computation of all discrete Fourier-related transforms. The short-time Fourier-related transforms are discussed for applications involving nonstationary signals. The one-dimensional transforms discussed are also extended to the two-dimensional transforms     

Bessel函数与三角函数之积的级数展开及在微波滤波器中的应用

根据对平面波函数运用Fourier-Bessel定理,经过一系列推导并进行反Fourier变换,得到了直角坐标系下Bessel函数与三角函数之积的一种级数展开,该表达式应用到矩-圆波导结的计算中,能解析地推出其广义S参数,得到与文献和HFSS软件较为一致的结果.计算了Ku和Ka频段多种尺寸的有厚度的矩形孔的耦合系数,并与文献、实验数据进行了比较,吻合较好,设计了一个Ku频段6阶类椭圆函数滤波器,实验性能与理论结果一致.     

Sampling theorem for finite-energy signals (Corresp.)

It is shown that the Shannon sampling expansion for finite-energy bandlimited signals is a special case of the Parseval relation for complex Fourier series.     

迂回相位编码的傅里叶变换计算全息图及其再现

光学全息图直接利用光学干涉法在记录介质上记录物光波和参考光波叠加后形成的干涉图样,而采用计算全息(CGH)的方法可不借助参考光直接记录物光波的复振幅信息。如果对迂回相位编码的全息图再进行一次逆的快速傅里叶变换,则可由计算机模拟完成物光波的全息图再现。试验结果也验证了该方法的可行性。     

A fast algorithm for linear estimation of two- dimensional isotropic random fields

The problem considered involves estimating a two-dimensional isotropic random field given noisy observations of this field over a disk of finite radius. By expanding the field and observations in Fourier series, and exploiting the covariance structure of the resulting Fourier coefficient processes, recursions are obtained for efficiently constructing the linear least-squares estimate of the field as the radius of the observation disk increases. These recursions are similar to the Levinson equations of one-dimensional linear prediction. In the spectral domain they take the form of Schrödinger equations, which are used to give an inverse spectral interpretation of our estimation procedure.     

EM alignment using phase for secure embedded systems

If electromagnetic (EM) waves emanating from a wireless device during a cryptographic computation leak sufficient information, it may be possible for an attacker to reconstruct the secret key. Despite the complexities of a Java-based PDA device, this paper presents a new phase based technique for aligning EM frames for subsequent time based DEMA. The proposed technique involves: fast Fourier transform, phase-substitution, inverse fast Fourier transform and time based DEMA. Results are repeatable over several different secret keys. Unlike previous research the new technique does not require perfect alignment of EM frames, and demonstrates robustness in the presence of a complex embedded system (including cache misses, operating system events, etc.) with random delays as well as random operations. This research is important for future wireless and complex embedded systems where security is crucial.     

Rate allocation for spotlight SAR phase history data compression

Complex phase history data in synthetic aperture radar (SAR) systems require extensive processing before useful images can be obtained. In spotlight mode SAR systems, useful images can be obtained by applying aperture weighting and inverse Fourier transform operations to SAR phase history data. In this paper, we are concerned with the compression of the complex phase history data obtained by a spotlight SAR system. We exploit knowledge of the aperture weighting function along with Fourier transform processing to attach a "gain" factor to each complex phase history data sample. This gain factor is then used to efficiently allocate bits to the phase history data during quantization. Performance evaluations are presented for this compression system relative to other existing SAR phase history data compression systems.