信号系统期末试卷（一）
1. （12 point） consider the system illustrated in Figure 1, where . Suppo the input determine the output.
Figure 1
Solution:
2. （10 point） Consider the system illustrated in Figure 2, suppo is shown in Figure 3.
(a) Determine the maximum sampling interval T such that is recoverable from
(b) If cond, sketch the spectrum of
(c) If cond, determine a filter so that
婚庆专用歌曲Solution: (a)
So, it shall be satisfied with
(b) If, then
(c) If, then
3. （8 point） Let denotes the Fourier transform of the signal depicted in Figure 4.
(a) Find
(b) Find
(c) Find
Solution:
(a) is a real and odd signal. This implies that
is an imagery and odd signal.
,
Also,.
(b)
(c)
4. （6 point） Determine the function, for the Laplace transform and its associated regions of convergence:
春节儿童简笔画, ROC:
Solution:
5. （12 point） Consider an LTI system with input and output
(a) Find the system function, indicate the ROC of
(b) Determine the unit impul respon, is this system stable?
(c) Compute the output of this system, if the input signal is
Solution:
(a)
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, ROC:
(b)
Stable!
(c)
6. （12 point） The input and output of a stable LTI system are related through the block-diagram reprentation shown in Figure 5.
现代女子医院(a) Determine the system function, indicate the ROC of
(b) Determine the unit impul respon of this system, is this system causal?北京奥运吉祥物
(c) For the input, compute the output.
Solution:
修改mac (a) , ROC:
(b) , Causal
(c)
附：梅森公式
信号流图的特征行列式，且有
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表示由源点到输出点之间第条前向通路的标号
表示由源点到输出点之间第条前向通路的增益
表示对于第条前向通路特征行列式的余因子。它是除去与第条前向通路相接触的环路外，余下的子图特征行列式。将欲辞君挂帆去
