1、学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 1 页 共 5 页电子科技大学 2013-2014 学年第 1 学期期 中 考试 卷课程名称：_数字信号处理 考试形式： 开卷 考试日期： 2013 年 11 月 日 考试时长：120 分钟课程成绩构成：平时 20 %， 期中 20 %， 实验 20 %， 期末 40 %本试卷试题由_6 部分构成，共_5_页。题号 一 二 三 四 五 六 合计得分1、Determine whether each of the following sequences is periodic or not. If it is, give
2、the fundamental period.(a) 25jnxe(b) si19(c) jnxe(d) jSolution：（a） is periodic, and ,N=5 is the fundamental period.025（b） is periodic, and ,N=38 is the fundamental period.03819（c） is not periodic.（d） is not periodic.2、Known an LTI system with and shown as figure 2.1. When an input is 1jHeargjHe3cos2
3、4xnndetermine the output yn.Figure 2.1得 分得 分 32slope 1k23slope 1k argjHe学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 2 页 共 5 页Solution：33242424241111jnjnjnjjnjxneeee2424242411cosjnj jnjj jjnjnyee 3、A digital signal processing system is represented as figure 3.1. The frequency spectrum of an analog input si
4、gnal ()aXjis given in figure 3.2. The analog signal is being sampled at sampling interval . And pass the sampled sequence gn through ()axt43mTan ideal lowpass filter with cutoff frequency , as shown in figure 3.3. Then put the filters output yn into the ideal ()jHe 2mcTinterpolator, an analog output
5、 can be got. Please sketch:(ayt(1) The frequency spectrum of the sampled sequence gn.)jGe(2) The frequency spectrum of the filter output yn.(jY(3) The frequency spectrum of the system output .)aj()aytSolution： 3424,33ms mmTTT得 分Ideal Sampler ()jHeIdeal Interpolator()axt gnyn()aytFigure 3.1 A digital
6、 signal processing systemcc0 ()jHeFigure 3.3 The spectrum of ideal lowpass filter1m2m()aXjFigure 3.2 Spectrum of ()axt010.5学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 3 页 共 5 页4、An LTI system has the unit impulse response ,where and hn12hn1sin(0.2)hn. is the frequency response of the system.2sin(0.8)h()jH
7、e(a) Try to plot the frequency response of another system with the unit impulse response .2ngh(b) Try to plot the frequency response of the 3-rd system with the unit impulse response .(1)nf(c) Compute the value of . 2nhSolution：得 分学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 4 页 共 5 页5、Suppose being the DT
8、FT of the sequence . And is a 10-point finite-length sequence, ()jXe 12nxuynthat is, and . is the 10-point DFT of , which corresponds to 10 samples of 0,yn0,1ynYkwith equal interval. Determine . ()jeSolution：221010101,2jkjknj knj nXeYkXxexWIts 10-point IDFT is：99 91010 10001 klnknklnkkl llnkryYWxWxr
9、 得 分学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 5 页 共 5 页101010,9lr rrynxnlrxnxnr 10 1010222,94,23 nr r rnnu6、Suppose we have two length-4 sequences and , defined as following:xnhcos,0,1232,nh(a) Compute and sketch which is the 4-point DFT of .Xkx(b) Sketch the 4-point IDFT of .41Fk(c) Let be the 4-point
10、DFT of , and be the real part of .Sketch the 4-point IDFT of . HkhnReGHkHkGk(d) Let the circular convolution ,and the linear convolution . Cyx560mhnxhnLynx30mhxhnPlease give out the points where for .LnSolution:(a) 1,02xnSo 3324 2000NjknNjkn jknnXkexee 11,kjk(b)得 分学院 姓名 学号 任课老师 考场教室_选课号/座位号 密封线以内答题无效第 6 页 共 5 页(c)(d)
