信号与系统习题集英文版

信号与系统习题集

第一部分：时域分析

一、填空题

1. =---)3()()2(t t u e t δ ( )。

2. The unit step response )(t g is the zero-state response when the input signal is

( ).

3. Given two continuous – time signals x(t) and h(t), if their convolution is denoted by y(t), then the convolution of )1(-t x and )1(+t h is ( ).

4. The convolution =+-)(*)(21t t t t x δ( ).

5. The unit impulse response )(t h is the zero-state response when the input signal is

( ).

6. A continuous – time LTI system is stable if its unit impulse response satisfies the condition: ( ) .

7. A continuous – time LTI system can be completely determined by its ( ). 8. =⎰∞∞-(t)dt 2sin 2 δt

t ( ). 9. Given two sequences }1,2,2,1{][=n x and }5,6,3{][=n h , their convolution =][*][n h n x ( ).

10. Given three LTI systems S1, S2 and S3, their unit impulse responses are )(1t h , )(2t h and )(3t h respectively. Now, construct an LTI system S using these three systems: S1 parallel interconnected by S2, then series interconnected by S3. the unit impulse response of the system S is ( ).

11. It is known that the zero-stat response of a system to the input signal x(t) is ⎰∞-=t

d x t y ττ)()(, then th

e unit impulse response h(t) is ( ). 12. The complete response o

f an LTI system can be expressed as a sum of its zero-state response and its ( ) response.

13. It is known that the unit step response of an LTI system is )(2t u e t -, then the unit impulse response h(t) is ( ). 14. =++-=⎰∞dt t t t t x ))1()1((2

sin )(0δδπ

( ). 15. We can build a continuous-time LTI system using the following three basic

operations: ( ) , ( ), and ( ).

16. The zero-state response of an LTI system to the input signal )1()()(--=t u t u t x

is )1()(--t s t s , where s(t) is the unit step response of the system, then the unit impulse response h(t) is ( ).

17. The block diagram of a continuous-time LTI system is illustrated in the following figure. The differential equation describing the input-output relationship of the system is ( )。

18. The relationship between the unit impulse response h(t) and unit step response s(t) is s(t) = ( ), or h(t) = ( ).

19. If the unit impulse response h(t) of

二、选择题

1. For each of the following equations, ( ) is true.

A 、)()()1(t t t δδ=-

B 、)(2)1()1(t t t δδ=-+

C 、⎰∞∞-=+)()()1(t dt t t δδ

D 、⎰∞

∞-=++1)1()1(dt t t δ 2. Given two continuous-time signals )(t x and )(t h , if the convolution of )(t x and )(t h is denoted by )(t y , then the convolution of signals )1(+t x and )2(-t h is

( ).

A 、)(t y

B 、)1(-t y

C 、)2(-t y

D 、)1(+t y 3. The unit impulse response of an LTI system is h(t) = t e

-, this system is ( ).

A. causal and stable

B. causal and unstable

C. noncausal and unstable

D. noncausal and stable

4. dt t t t x )2()12()(112

-+=⎰-δ = ( ).

A 、1

B 、3

C 、9

D 、0

5. For an LTI system, if the input signal is )(1t x , the corresponding output response is )(1t y , if the input signal is )(2t x , the corresponding output response is )(2t y .

)(t y