信号与系统signal and system英文版往年考试题1

参考答案

I. Blank filling (Total scores 60, each scores 5. ) 1、

1f(0)（70％） a2、

1/2（96％）

3、

etu(t)(t)（92％）

4、Piecewise function can be comprised by rectangular window functions(可以用矩形窗函数构造分段函数). Consider a signalf(t)t[u(t)u(t1)]，the even component of f(t) is fe(t)＝ ，the odd component of f(t) is

fo(t)＝

t[2u(t)u(t1)u(t1)]（46％） 2t[u(t1)u(t1)]（92％） 25、Consider a signal e(t)t[u(t)u(t1)]，and

h(t)et[u(t)u(t1)]，so e(t)*h(t) 。

(Express your answer by rectangular window function like

I.4) 先做微分

t1et,0t1y(t)e1(2t),1t20,其他e112（76％）

6、Necessary and sufficient conditions for stability of the system

is

its

impulse

response

h(t)should be

【int(f(x),-inf,inf)＝f(x)dx】

h(t)dt（37％）

7、consider a signal e(t)u(t)u(t1)，则e(t)*e(t) (Express your answer by rectangular window function like I.4)

t[u(t)u(t1)](2t)[u(t1)u(t2)] （87％）

t,0t12t,1t20,others

8、Known Fourier transform of f(t) is F(j)，so the Fourier transform of f(4t) is 。

ej4F(j)（71％）

9、The Fourier transform of ej2t'(t) is (t)1'(t)jej2t'(t)j(2)（83％）

10、A system S with input x[n] and output y[n] related by

y[n]x[n]{g[n]g[n2]} is time invariant while

g[n]= . Constant（6％）

11、x(t)(tT)(tT),y(t)x()d, thenE of

ty(t) is

2T（73％）

II. Single choice(Total scores 24, each scores 6. ) 1.The equivalent expression of (t24) is ( D )

1A：(t2)

2 B：[(t2)＋(t2)] D：[(t2)＋(t2)]

(t)dt1 (t)0(t0)121C：(t2)

4142. Refer to the Fourier transform of determine

x(t)eu(t), to

atf(t) when the Fourier transform of f(t) is

f(t) is ( B )

B：e(5j2)tu(t) D：e(5j2)t

1, then

5j(2)A：e(5j2)tu(t) C：e(5j2)t

1eu(t)

ajat3.The input e(t) and output r(t) of a continuous system is

regulated by r(t)=e(t+2), then the system is ( D ) A：causal, time-variant, linear, stable

B：causal, time-invariant, nonlinear, unstable C：non-causal, time-variant, linear, stable D：non-causal, time-invariant, linear, stable

4.The input f(t) and output r(t) of a system is governed by

r(t)f()ed, then the system is ( B )

A: Linear and time-invariant system B: Linear and time-variant system C: Nonlinear and time-invariant system D: Nonlinear and time-variant system

III. True or False. (Total score 16, each scores 2.) 1.If system input isx(t), then the systemlinear.

T

2.If h[n]k(for any n), and k is a known constant, then the LTI system with unit impulse response h[n] is stable.

F

3.The Fourier transform of real even signal is also a real even function.

T

4.For any system, the impulse response completely describes

y(t)tx(t) is

its behavior.

F

5.If h(t) is the unit impulse response of a LTI system, and h(t) is periodic and non-zero, then the system is unstable.

T

6.The summation of two periodic signals is also a periodic signal.

F

7.LTI system must be causal.

F

8. The Fourier transform of a real odd signal is a purely imaginary and odd function of frequency.

T