《信号与系统》
![](https://wkrtcs.bdimg.com/rtcs/image?w=29.533333333333&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"29.533333333333","h":"29.533333333333","dataType":"png","c":"word/media/image1_1.png","imgOriW":221,"imgOriH":222})
须知：符号?(t)、?(k)分别为单位阶跃函数和单位阶跃序列。LTI表示线性时不变。 为加法器。
一、单项选择题（每小题4分，共32分）
D 1、序列和![](https://wkrtcs.bdimg.com/rtcs/image?w=145&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"145","h":"68","c":"4a7bf2b2b2bdfede7ee850887faeef2f.png"})
A．3? (k–2) B．3? (k) C．1 D．3
D 2、积分![](https://wkrtcs.bdimg.com/rtcs/image?w=147&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"147","h":"58","c":"f7395584b5ba50b6ce3f4f0e9abe2415.png"})
A．0 B．1 C．e D．e2
B 3、![](https://wkrtcs.bdimg.com/rtcs/image?w=107&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"107","h":"21","c":"31faf0c2aa465a255921d6da0d08c3bd.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=84&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"84","h":"21","c":"a978a499dfe66f1719883a87d1063a75.png"})
B 4、![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"48","h":"23","c":"27f85290bff93f2314fdde37ce4d2584.png"})
题4图
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"16","h":"43","c":"93b05c90d14a117ba52da1d743a43ab1.png"})
B 5、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=167&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"167","h":"23","c":"f670c17d9d99ff1515fd8c478a2b0c68.png"})
题5图
A．1 B．2 C．3 D．4
D 6、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=145&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"145","h":"21","c":"3ee9e8b6e8489c73681475b90e05a93c.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=114&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"114","h":"43","c":"a73d0086d0013798875400956aa28b2c.png"})
D 7、已知单边拉普拉斯变换的象函数![](https://wkrtcs.bdimg.com/rtcs/image?w=106&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"106","h":"43","c":"c68bdaca296b18f129a9de9bd61c2992.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=69&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"69","h":"22","c":"99a564e53159ab69d069082ac0b65815.png"})
B 8、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=112&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"112","h":"21","c":"4b43b221e008c0861f581fe24a380845.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=42&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"42","h":"43","c":"76f679160717e6c55e8c81646991a8d2.png"})
二、填空题（每小题5分，共30分）
9、单边拉普拉斯变换定义![](https://wkrtcs.bdimg.com/rtcs/image?w=60&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"60","h":"21","c":"e9c5a88d1dbbadd516ac25e71c63d676.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=514.66666666667&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"514.66666666667","h":"150.66666666667","dataType":"gif","c":"word/media/image41.gif"})
10、已知
(1) (2)
11、已知象函数![](https://wkrtcs.bdimg.com/rtcs/image?w=157&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"157","h":"43","c":"d3c69ff753f43acc75ff067b584bf783.png"})
12、![](https://wkrtcs.bdimg.com/rtcs/image?w=169&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"169","h":"22","c":"5bf6f549ec2014fbe83d06d2fc48db48.png"})
13、已知信号流图如题13图所示，则系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=62&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"62","h":"21","c":"79215479f32a2bb2194e95a502f3580e.png"})
题10图 题13图
14、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"40","h":"21","c":"d6e3af948a34fd5f432cb9d377a98ef0.png"})
三、计算题（38分）
请你写出简明解题步骤；只有答案得0分。非通用符号请注明含义。
15、已知
解:对等式两边取拉普拉斯变换, 得: ![](https://wkrtcs.bdimg.com/rtcs/image?w=162&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"162","h":"48","c":"a046077257c9a17be9ec877b00957b29.png"})
则 ![](https://wkrtcs.bdimg.com/rtcs/image?w=98&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"98","h":"43","c":"04d140364e2ba8ee44d9ccb17c3c4952.png"})
再由拉普拉斯反变换,得![](https://wkrtcs.bdimg.com/rtcs/image?w=122&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"122","h":"22","c":"6312ee9adf08e4dbfd594422d7ad2ed8.png"})
16、描述某LTI系统的微分方程为（10分）
y"(t) + 5y'(t) + 6y(t) =f (t)
已知初始状态y(0-) = 1，y'(0-)=－1，激励f (t)= e-t?(t)，求：
（1）求系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=46&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"46","h":"21","c":"f68021749ff69bf0b89869d4358ea300.png"})
（2）求系统的冲激响应；
（3）已知初始状态y(0-) = 1，y'(0-)=－1，激励f (t)= e-t?(t)，求系统输出的全响应![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"43","h":"21","c":"0707669836d19443cf6c5cc89ca963e6.png"})
解:
(1) 由微分方程y"(t) + 5y'(t) + 6y(t) =f (t)可得系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=145&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"145","h":"43","c":"2e652a2e4004346c4f647a18b0a8c5cd.png"})
(2) 系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=38.4&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"38.4","h":"19.2","dataType":"png","c":"word/media/image63_1.png","imgOriW":896,"imgOriH":512})
反拉普拉斯变换得系统的冲激响应
(3) 零状态响应为![](https://wkrtcs.bdimg.com/rtcs/image?w=513&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"513","h":"44","c":"f437c4b79772e7b700220669874cb4d5.png"})
则![](https://wkrtcs.bdimg.com/rtcs/image?w=318&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"318","h":"28","c":"643d3e5f1a347fc8af1efc2126838b8d.png"})
零输入响应为![](https://wkrtcs.bdimg.com/rtcs/image?w=194&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"194","h":"28","c":"572f26dfd49a4b89295e9299617f3f3c.png"})
代入初始条件y(0-) = 1，y'(0-)=－1得![](https://wkrtcs.bdimg.com/rtcs/image?w=117&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"117","h":"23","c":"052863a9d2df4883aef08f8c72ce4ff4.png"})
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=224&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"224","h":"28","c":"19dbf7dc08a873a1ce2757f4c90d2ae4.png"})
全响应为![](https://wkrtcs.bdimg.com/rtcs/image?w=441&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"441","h":"28","c":"971142db29eba1bac6849a2994974a3e.png"})
17、题17图所示离散系统，求：（10分）
（1）系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=47&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"47","h":"21","c":"76a83851ba32f09d9c47500acc0ba231.png"})
（2）列写该系统的差分方程。
题17图
解：（1）由上图得系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=265&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"265","h":"44","c":"b11295a591a1fc148e3b37d57b1028aa.png"})
（2）由系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=467&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"467","h":"44","c":"c77b8a43ca78f00a2c9100d7532ad27c.png"})
可得系统的差分方程为：
18、已知某LTI因果系统，其系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=125&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"125","h":"43","c":"c94768c2bc99533f1577d76354e92ae7.png"})
解：系统函数![](https://wkrtcs.bdimg.com/rtcs/image?w=99&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"99","h":"43","c":"31c6e03d47878e7f6156682ed924d979.png"})
输入信号的拉普拉斯变换![](https://wkrtcs.bdimg.com/rtcs/image?w=98&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"98","h":"43","c":"c3c665b9446b2e93613855f625c2229d.png"})
零状态响应的拉普拉斯变换为![](https://wkrtcs.bdimg.com/rtcs/image?w=400&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"400","h":"67","c":"355de6bcf4155749dcdfe8a39bff79ab.png"})
则系统的零状态响应为![](https://wkrtcs.bdimg.com/rtcs/image?w=262&md5sum=0831249f77ce4239e25207fde876fc65&sign=449c36b8cb&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=283&ipr={"t":"img","w":"262","h":"43","c":"82ab7a5846f895fcf47cb2c31335cf99.png"})
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