习题参考答案
7-1 求如下信号的频谱|F(i?)|。 (1)f(t)?1
(2)f(t)?e?t (4)f(t)?t (6)f(t)?tcost
(3)f(t)?cost (5)f(t)?te?t
解:控制系统中的信号都是指t?0时f(t)?0函数。以下信号不考虑频谱中的奇异信号。 (1)|F(i?)|?|(2)|F(i?)|?|(3)|F(i?)|?|(4)|F(i?)|?(5)|F(i?)|?1?|
11 |?21?i?1???|
1??21?2
1
(1??)21??2(6)|F(i?)|?
(1??2)27-2 对题7-1的信号进行采样,采样频率为T=0.1秒, (1)求采样信号的频谱|F(i?)|。 (2)求采样信号的z变换。
1
*解:
(1)f(t)?1
?f(t)???(t?0.1n)
*n?0F(i?)???*?e?i0.1n??n?0?11?e?i0.1?1
1?cos0.1??isin0.1?12?2cos0.1?1zF(z)??
1?z?1z?1(2)f(t)?e?t
f(t)??e?0.1n?(t?0.1n)
*n?0?F(i?)???*?e?0.1n?i0.1n??n?0?11?e?0.1?i0.1??0.111?e?0.1cos0.1??ie1sin0.1?
1?e?0.2?2e?0.1cos0.1?1zF(z)?? ?0.1?1?0.11?ezz?e(3)f(t)?cost
2
f(t)??(cos0.1n)?(t?0.1n)*n?0??*1(ei0.1n?e?i0.1n)?(t?0.1n)?2n?0?
1F(i?)?2??en?0??i0.1n(??1)??e?i0.1n(??1)n?0?111?21?e?i0.1(??1)1?e?i0.1(??1)12?e?i0.1(??1)?e?i0.1(??1)?21?e?i0.1(??1)?e?i0.1(??1)?e?i0.2?12?2e?i0.1?cos1?21?2e?i0.1?cos1?e?i0.2???(note:cos1?0.54)
1?0.54cos0.1??i0.54sin0.1?1?1.08cos0.1??cos0.2??i(1.08sin0.1??sin0.2?)1.29?1.08cos0.1?3.17?2.16cos0.1??2cos0.2??2.16cos0.1?cos0.2?1?0.54z?1z2?0.54zF(z)??2 ?1?21?1.08z?zz?1.08z?1(4)f(t)?t
f(t)??0.1n?(t?0.1n)
*n?0? 3
广西大学自动控制原理习题答案(本科)第7章
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