一种计算N阶滤波器响应的级数展开法

METHOD OF SERIES EXPANSION TO CALCULATE N-STAGE FILTER RESPONSE

本文用级数展开的方法，计算了Ｎ阶低通、带通和高通波波器的响应，将复杂的卷积积分大分简化，还讨论了误差及改进方法．在一定条件下，只取级数的前几项，就能很精确地描述系统响应．最后，还给出了高通滤波器的矩形脉冲和三角形脉冲的响应波形．

The responses of N-stage lowpass bandpass and highpass filters are calculated by themethod of series expansion in this paper. The method can simplify the caculation of convolutiongreatly. Also , the erros are discussed and the improvement is introduced. Under certain condition ,the actual responses of the systems can be discribed precisely only by the first a few terms of the se-ries expansion. This provides facilities for both theoretic analysis and applications. Finally , the re-sponse forms of highpass filters for rectangular pulse and triangular pulse are proviued.