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
