基于数学形态学的数字滤波器设计与分析

针对电力信号监测中可能遇到的各种干扰，通过数值仿真详细研究了结构元素的形状、幅值和宽度对形态学数字滤波器性能的影响。分析指出，最优结构元素的选取，与干扰的类型和频率、待处理数据序列的采样率等因素密切相关，一般要根据信号和干扰的具体特征，通过数值仿真预先确定。对于宽带干扰的消去，采用余弦型结构元素时滤波效果较好：对于窄带干扰的消去，矩形结构元素的应用特性较佳。随着信号采样频率的增加，结构元素宽度应按线性递增规律选取，以获得较优的滤波特性。这些研究结果为形态学滤波器在电力信号监测和处理中的应用提供了设计依据。

DESIGN AND ANALYSIS OF MATHEMATICAL MORPHOLOGY-BASED DIGITAL FILTERS

With respect to different types of the interference possibly encountered in power signal monitoring, detailed investigations are carried out through numerical simulation, regarding the impacts of the shape, amplitude and width of a structure element on the performance of mathematical morphology-based digital filters. The analysis indicates that, the selection of an optimal structure element is very much dependent on the type and frequency of the interference as well as the sampling rate of the data series to be processed, and should normally be pre-determined by numerical simulation based on the concrete features of both the signal and its interference. For an effective elimination of the wide-band interference, a structure element of cosine type should be preferably applied to obtain satisfying filter performance. But for the narrow-band interference, a rectangular structure element shows good behaviors in applications. Also, the width of a structure element should be chosen proportionally to the increase of the sampling rate to achieve optimal filtering characteristics. These research results present useful design references for the application of the mathematical morphology-based filters in power signal monitoring and processing.