Ch10-作业解答-2010

Ch10-作业解答-2010

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Ch10 习题参考解答 10-22 要求通过模拟滤波器设计数字低通滤波器,给定指标: -3dB 截止角频率 2 c ,通带内 0.4 p  处起伏不超过 -1dB ,阻带内 0.8 s 处衰减不大于 -20dB ,用巴特沃思滤波特性实现 1 用冲激不变法,最少需要多少阶? 2 用双线性变换法,最少需要多少阶? 解: 1 冲激不变法: 求模拟滤波器技术指标: 为方便起见,取 T=1s 0.4 rad/s p p T   0.8 rad/s s s T   0.5 rad/s c c T   按通带指标: 1 2 20 2 1 [ ] 10 1 ( ) p N c 0.1 lg(10 1) 3 0.4 2lg( ) 0.5 N  按阻带指标: 20 2 20 2 1 [ ] 10 1 ( ) N s c 2 4.89 0.8 ) 0.5 N  取两者的较小值,得 3 N 。此时通带满足指标要求,阻带留有余量。 2 双线性变换法: 求模拟滤波器技术指标:
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2 tan 2 tan 2 rad/s 24 c c T   2 tan 2 tan 0.2 1.4531 rad/s 2 p p T   2 tan 2 tan 0.4 6.1554 rad/s 2 s s T   按通带指标: 1 2 20 2 1 [ ] 10 1 ( ) p N c 0.1 lg(10 1) 2.115 1.4531 2lg( ) 2 N  按阻带指标: 20 2 20 2 1 [ ] 10 1 ( ) N s c 2 2 6.1554 ) 2 N 取两者的较小值,得 2 N 。此时阻带满足指标要求,通带略有余量。 10-26 试求汉宁窗函数的傅里叶变换,并解释旁瓣电平降低的原因。 解: 汉宁( Hanning )窗(升余弦窗): 12 ( ) [1 cos ] (0 21 n n n N N 所以 1 0 22 11 ( ) ( ) 00 1 ( ) ( ) 0 ( ) ( ) cos ] [ ] 1 1 1 [ ] 2 1 4 j j n H n N jn n nn NN j n j n jN
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This note was uploaded on 03/28/2011 for the course ELECTRICAL 30230104 taught by Professor Yongren during the Fall '11 term at Tsinghua University.

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Ch10-作业解答-2010

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