Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.This work was partially funded by The National Supercomputing Center for Energy and the Environment, University of Nevada Las Vegas, Las Vegas, Nevada and by NSF Grant MIP-9200581.     

参数化滤波器逼近问题的棱柱算法

本文基于多胞形上D.C.函数的棱柱算法,给出了一维参数化小波滤波器逼近问题的一种算法.     

On timing Jitter in wavelength-division multiplexed soliton systems

Collision-induced timing shifts in a wavelength-division multiplexed soliton system are computed when damping, amplification, filtering and positive dispersion management following the loss profile are included. A statistical analysis is presented which takes into account the resulting effect of the large number of collisions occurring in the fiber. Analytic expressions are derived for the root mean square timing jitter and the maximum length of error-free transmission with an arbitrary number of channels. An extensive analysis of system performance corresponding to situations with and without filters and/or dispersion management is carried out.     

A study of the optical transfer function for annular binary filters

The annular binary pupil filters consist of two transparent annuli obstructed by an annular mask. The optical transfer functions for them are analytically derived under paraxial approximation, and three- and two- as well as one-dimensional numerical plots are presented. It is shown that by changing the parameters of transparent regions it is possible to improve the axial resolution whilst the transverse resolution remains unchanged, compared with an annular lens. Results indicate, as is well known, that this kind of filters can be applied to three-dimensional confocal microscopy.     

On Optimal Defuzzification and Learning Algorithms: Theory and Applications

In this paper, the issue of optimal defuzzification which is advocated in the Optimality Principle of Defuzzification (Song and Leland (1996)) is addressed. It was shown that defuzzification can be treated as a mapping from a high dimensional space to the real line. When system performance indices are considered, the defuzzification mapping which optimizes the performance indices for the given fuzzy sets is known as the optimal defuzzification mapping. Thus, finding this optimal defuzzification mapping becomes the essence of defuzzification. The problem with this idea, however, is that the space formed by all possible continuous defuzzification mappings is so large to search that the only recourse is an approximation to the optimal defuzzification mapping. With this, learning algorithms can be devised to find the optimal parameters of defuzzifiers with fixed structures. The proposed method is rigorously examined and compared with some well-known defuzzification methods. To overcome the resultant enormous computational load problem with this algorithm, the concept of defuzzification filter is additionally proposed. An application of the method to the power system stabilization problem is presented.     

Design and Characterization of Novel Comb Filters Based on Periodical Fiber Bragg Gratings

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Design Method for Optical Waveguide Filters Having Corrugation Structures by Corrugation Width Modulation

A method to design a corrugated optical waveguide filter by modulating the corrugation width profile is proposed. This method is based on combined applications of the Fourier transformation and the F-matrix formalism. The method achieves the spatial profile of the corrugation width required to design a filter with any specified spectral profile of the reflection coefficient. The idea of the technique is that the spatial variation of the effective refractive index can be transformed, with the help of the F-matrix formalism, to variation of the corrugation width while maintaining a constant amplitude of the refractive index variation. Two examples are given applying the technique to the design of optical waveguide filters with reflectivity profiles of two- and four-rejection bands.     

Optical-digital processors for morphological and rank order filtering

Non-linear rank order and morphological filtering can be achieved in optical-digital processors. In these processors, all convolutions are performed in inherently parallel optical correlators. Arithmetic and logic operations are made digitally. Due to the threshold decomposition concept, grey scale images are sequentially treated slice by slice. The optical-digital method of local histogram calculation within both binary and weighted neighbourhoods allows local non-linear operations. We derive rank order and morphological filters from optically calculated convolutions. Several configurations of optical convolvers are discussed. Further improvements in the technology of spatial light modulators and encoded light sources are needed before these processors' practical uses will appear.     

基于矢量衍射理论的相位型光瞳滤波器设计

根据矢量衍射理论,提出了一种设计纯相位型光瞳滤波器的新方法根据该方法所设计的滤波器主要应用于采用高数值孔径显微物镜的成像系统对点扩散函数中的指数因子进行二次近似处理后,可以得到超分辨参量与滤波器参量的近似关系式以三区相位型滤波器为例,讨论了该近似关系式的有效性给出一个设计实例,根据所要求的超分辨性能要求设计滤波器.模拟结果表明,该滤波器达到了设计要求,最后利用共焦系统点扩散函数的乘积特性,大大减弱了旁瓣的影响.     

利用三色光栅实现彩色图像相减

本文提出了一种彩色图像相减的新方法.该方法利用互相错动半个周期的两组三色光栅,在黑白底片上分别对待处理的两幅图像进行一次编码记录,然后在白光处理器上对黑白编码片进行彩色译码,即可实现彩色图像的强度相减,文中讨论了三色光栅实时生成和两组三色光栅条纹自动错动半个周期的方法,并给出了实验结果。