信号与系统习题集18359

信号与系统练习题集 第一部分：信号与系统的时域分析

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 the unit impulse response h(t) is ( ).

12. The complete response of 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 is

h(t) = ( ).

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) = ( ).

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 ( ).

)(t