电子科技大学2013数字信号处理半期考卷(含答案).docVIP

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 the fundamental period. (a) (b) (c) (d) Solution： is periodic, and ,N=5 is the fundamental period. is periodic, and ,N=38 is the fundamental period. is not periodic. is not periodic. 2、Known an LTI system with and shown as figure 2.1. When an input is determine the output y[n]. Figure 2.1 Solution： 3、A digital signal processing system is represented as figure 3.1. The frequency spectrum of an analog input signal is given in figure 3.2. The analog signal is being sampled at sampling interval . And pass the sampled sequence g[n] through an ideal lowpass filter with cutoff frequency , as shown in figure 3.3. Then put the filter’s output y[n] into the ideal interpolator, an analog output can be got. Please sketch: (1) The frequency spectrum of the sampled sequence g[n]. (2) The frequency spectrum of the filter output y[n]. (3) The frequency spectrum of the system output . Solution： 4、An LTI system has the unit impulse response ,whereand . is the frequency response of the system. (a) Try to plot the frequency response of another system with the unit impulse response. (b) Try to plot the frequency response of the 3-rd system with the unit impulse response. (c) Compute the value of. Solution： 5、Suppose being the DTFT of the sequence . And is a 10-point finite-length sequence, that is, and . is the 10-point DFT of , which corresponds to 10 samples of with equal interval. Determine . Solution： It’s 10-point IDFT is： 6、Suppose we have two length-4 sequences and , defined as following: Compute and sketch