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电 子 科 技 大 学 二O O六 至 二O O七 学年 第一学期（阶段测试）
SIGNALS AND SYSTEMS 课程考试试题(120分钟) 考试日期：2006年 11 月12 日
一 二 三 四 五 六 七 八 九 十 总分 评卷教师
Attention: each of the following questions may have more than one right answers, justify your answers and write it in the blank. 1. ??? 0cos2?t??2t?2?dt?( ). (a) 1 (b) －1 (c) －0.5 (d) 0.5 2. The period of x?n??cos??n/2??sin?n/2? is ( ). (a) N?2 (b) x?n? is not periodic. (c) N?3 (d) N?4 3. The convolution integral y?t??cost?eu?t? may be ( ). ?t(a) cos?t??/4? (b) 11cos?t??/4? (c) cos?t??/4? (d) cos?t??/4? 224. The closed-form expression for (a) u?t???t?2????t?3? dx?t? illustrated in Figure 1 is ( ). dtx(t)1(b) u?t???t?3????t?3? (c) u?t??2?t?1????t?3? 0123t(d) u?t???t?1????t?3? Figure 1 5. Let x?t? be a periodic signal with fundamental frequency ?0 and Fourier series coefficients ak. The Fourier series coefficients of x?t/2?3? is ( ). (a) ak/2 (b) 1ake?j3k?0 (c) ake?j3k?0 (d) 2ake?j3k?0 2共 4 页 第 1 页
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6. Consider an LTI system whose input x?n? and unit impulse response h?n? are
given by x?n??u?n?1??2?n?1??u?n?2?，h?n????n?1????n?1?
The output y?n??x?n??h?n? of this system is ( ).
(a) y?n???1,0,1,0,?1?,n??2,?1,0,1,2
(b) y?n???1,0,0,0,?1?,n??2,?1,0,1,2
(c) y?n???1,0,0,0,?1?,n??1,0,1,2,3
(d) y?n???1,0,?1,0,?1?,n??2,?1,0,1,2
7. Let x?t??u?t??u?t?1? , h?t??x?t/2? , y?t??x?t??h?t? may be ( ).
(a) ?t?1?u?t?1???t?2?u?t?2???t?3?u?t?3???t?4?u?t?4?
(b) tu?t???t?1?u?t?1???t?2?u?t?2???t?3?u?t?3?
(c) ?t?1?u?t?1???t?2?u?t?2???t?3?u?t?3???t?4?u?t?4?
(d) tu?t???t?1?u?t?1???t?2?u?t?2???t?3?u?t?3?
?t8. Consider an LTI system with unit impulse response ht?eu?t?， if the input ??
d??t? x?t?????t?, the output y?t? is ( ). dt
d??t? (a) ??t? (b) (c) e?tu?t????t? (d) ???t? dt
9. Consider an LTI system with unit impulse response h?t??u?t?1??u?t?2?， if
the input x?t? is illustrated in Figure 2 , the output y?t? t?0 is ( ).
x?t?(a) 0.5 (b) 1 (c) 1.5 (d) 0 1
t1?120?2
Figure2
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10. Consider an LTI system whose response to the signal
x1?t??tu?t??2?t?1?u?t?1???t?2?u?t?2? is the signal y1?t??costu?t?. If the
input x2?t? is illustrated in figure 3, the output y2?t? is ( ).
x2(t)(a) y2?t???costu?t??sint??t?
1(b) yt??sintut?costut??????2
t021(c) y2?t???cosu?t????t?
?1
(d) y2?t???sintu?t????t? Figure 3
11. Consider a continuous-time LTI system which frequency response is illustrated in
figure 4. When the input to this system is a periodic signal x?t? with fundamental
period T=1 and Foureier series coefficients ak, it is found y?t??x?t?. The input
signal x?t? must satisfy ( ).
H(j?)?0 , k?0? (a) ak?? (b) ak?0,k?0
1? 0 , k?0
?1/2?1/2????0(c) (d) xtdt?0xtdt?0???? ?1/2 0Figure 4
12. Consider a continuous-time system with input x?t? and output y?t? related by
2 y?t???xt?xt?1???????, this system may be ( ). (a) linear (b) time-invariant (c) not causal (d) stable
??共 4 页 第 3 页
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...... ...... ...... ...... ...... ......密...... ......封...... ......线...... ......内...... ......答...... ......题...... ......无...... ......效...... ...... ............ ...... ...... 12. Determine which of the following signals wish finite total energy ( ).
?t(a) xt?eu?t? (b) x?t??costu?t? ??
t(c) xt?eu?t? (d) x?t??cost????u?t??u?t?2???
13. The output of the system ( ) to the input x?t??cos2?t?sin5?t?cos10t is not
periodic. H(j?)H(j?) 1 1 ?? 003?3?4??3??4??3?
(a) (b)
H(j?)H(j?)
1 1
??4???3?04?03?(c) (d)
14. Consider a continuous-time LTI system whose frequency response is H?j???sin??/2??.
When the input to this system is x?t??ej?0t, it is found y?t??0. Which of the following
statements is ture ( ). (a)
?0?2? (b) ?0?? (c) ?0?3? (d) ?0?4?
15. We are given a certain LTI system with unit impulse response h0?t?,and
y0?t??x0?t??h0?t?. Which of the following statements is false( ).
(a) x0??t??h0?t??y0??t? (b) x0??t??h0??t??y0??t? (c) x0?2t??h0?t??y0?2t? (d) ?
?????tx0???d???h0?t???y0???d?
????t共 4 页 第 4 页