一、选择题（4分/每题，共20分）

1. Determine the output of the systems described by following differential equation:

)(4d )

(d )(2d )(d 3d )(d 22t x t t x t y t t y t t y +=++

)()(3t u e t x t

-=，

,0d )

(d ,1)0(0===t t t y y )()23()(2t u e e t h t t ---= Determine zero-initial response )(t y zi and zero-state response )(t y zs ：

（ ）

（A ）0,2)(2≥-=--t e e t y t

t

zi ,)

()21223()(32t u e e e t y t t

t zs ---+-=， （B ）0,2)(2≥-=--t e e t y t t zi ,)

()22

3

()(2t u e e t y t t zs ---= （C ）0

),2()(2≥-=--t e e t y t

t

zi ,

)()21223()(32t u e e e t y t t

t zs ---+-= （D ）

0),2()(2≥-=--t e e t y t t zi ,)

()2()(2t u e e t y t

t zs ---=

2. Evaluate the following discrete-time convolution sums:

]3[*]3[][y -+=n u n u n = ( )

(A)

][n nu

(B)

][1n u n ）（+ (C)

]3[1++n u n ）（ (D)

]3[1-+n u n ）（

3. The FS of )(t x is )(ωj X , the FS of ( ) is ωωj e j X -)2(.

(A)

)21

21(21-t x (B) )21(21-t x (C) )212(-t x (D) )1(2

1

-t x

4. The frequency response of a LTI system is ω

ω

ωj 1j 1)j (+-=

H , it is distortionless transmission or not? Determine the system output if the input is x (t )=sin t +sin3t (-∞<t <∞) . ( )

(A) it is distortionless transmission; )π7952.03sin()2/πsin()(-+-=t t t y (B) it is not distortionless transmission; )π7952.03sin()2/πsin()(-+-=t t t y (C) it is distortionless transmission; )3sin()sin()(t t t y +=

(D) it is not distortionless transmission; )3sin()sin()(t t t y +=