电子科大2010年信号与系统期末考题及标准答案1

………密………封………线………以………内………答………题………无………效……

电子科技大学二零 一 零 至二零 一 一 学年第 一 学期期 末 考试

SIGNALS AND SYSTEMS 课程考试题 A 大纲A 卷 （ 120 分钟） 考试形式： 一页纸开卷 考试日期 20 年 月 日

课程成绩构成：平时 10 分， 期中 20 分， 实验 10 分， 期末 60 分

一 二 三 四 五 六 七 八 九 十 合计 复核人签名

得分

签名

Attention: You must answer the following questions in English.

1.（15 points ） Suppose ()1x t and ()2x t are two band-limited signals, where

πωω200,0)(1>=for j X ,πωω500,0)(2>=for j X .

Impulse-train sampling is performed on ()()()1234/22=+-*y t x t x t to obtain ()()()p n y t y nT t nT δ+∞

=-∞

=

-∑.Give out the expression of

)(ωj Y in terms of )(1ωj X and )(2ωj X ，where )(ωj Y

is the Fourier transform of )(t y . Specify the largest values of the sampling period T

which ensures that ()t y is recoverable from ()t y p .

………密………封………线………以………内………答………题………无………效……

2.（20 points ）Consider a stable system illustrated in Figure 1, if we know )()(0t u e t h t

-=，()()1sin 5ππ=

t h t t , ()()

2sin 3ππ=t h t t

and the input ()()/2δ+∞

=-∞

=

-∑n x t t n ，determine the output ()y t .

Figure 1

3. ( 10 points ) Determine the function of time, []x n , for the Z transform ()X z and its associated regions of convergence:

()4

1

1X z z -=

- 1z >

)(0t h )

(t x )

(t y )

(1t h )

(2t h +

+

-

………密………封………线………以………内………答………题………无………效……

4.（15 points ）Consider a system illustrated in Figure 2(a). The input signal has the Fourier tansform ()X j ω shown in Figure 2(b), and the output signal has the Fourier tansform ()ωY j shown in Figure 2(c). Determine a possible system S.

()

y t Figure 2(a)

()

x t S

ω

ππ

-1

()X j ωFigure 2(b)

Figure 2(c)

ω

01

()

ωY j 4π3π

4π-3π

-

………密………封………线………以………内………答………题………无………效……

5.(20 points) Consider a LTI system with unit impulse response ()()()β--=+t t h t e u t e u t ,where β is an unknown constant. When the input to the system is ()1=x t ,the output is ()43

=

y t . (a) Determine the system function ()s H of the system and sketch the pole-zero pattern, then indicate the ROC of ()s H . (b) Is this system causal and stable ?

(c) Draw a block diagram representation of this system.

………密………封………线………以………内………答………题………无………效……

6.(20 points) A stable LTI system is described by the difference equation

[][][][]1271

42

--+

-=y n n y n x n y . (a) Find the system function ()H z , sketch the pole-zero pattern of ()H z , then indicate the ROC of ()H z . (b) Determine the unit impulse response []h n . Is this system causal? (c) Compute the output of this system, if the input signal is []cos x n n π=.