数字信号处理期末考试A卷答案.doc

精品文档学院_ 系别_ 班次_ 学号_ 姓名_.密.封.线.以.内.答.题.无.效.电子科技大学二零零 八 至二零零 九 学年第 一 学期期 末 考试数字信号处理课程考试题 半期考卷 （ 120 分钟） 考试形式： 开卷 考试日期 2008年12月 30 日课程成绩构成：平时 20 分， 期中 20 分， 实验 20 分， 期末 40 分一二三四五六七八九十合计1. Given a causal system with the transfer function being.(1) Try to calculate its difference equation.(2) Try to give the zero-pole plot of the system, then determine whether the system is stable.(3) Calculate its impulse response.(4) Give a canonic direct realization of the system and plot it.Solution: （共20分）(1) Difference equation is: 2yn-5yn-1+2yn-2=-3xn-1（3分）(2) zero-pole plot:（5分）The ROC is |z|2, so the system is not stable.（2分）(3) （5分）(4)z-1z-12.5xn-1-1.5ynxn-1.5yn2.5z-1z-1-1（5分）2.Consider a length-9 sequence xn = 2, -3, -1, 0, -4, 3, 1, 2, 4, -2 n 6. The z-transform X(z) of xn is sampled at N points wk = 2pk/N, 0 k N -1, on the unit circle yielding the frequency samples:Determine the periodic sequence whose discrete discrete Fourier series coefficients are given by when N = 4 and N = 11, respectively ( without evaluating ).Solution:（共15分） According to the definition of z-transform,（5分） Then, can be written as（5分） According to the definition of DFS（5分）when N = 4, , and its principle period is 0, 2, 2, 0, 0 n 3when N = 11, , and its principle period is -1, 0, -4, 3, 1, 2, 4, 0, 0, 2, -3, 0 n 103Knowing the transfer function of a causal system as , we get a new transfer function . Please:(1) Sketch the magnitude response of .(2) Determine the values of peaks and dips in magnitude of .(3) If the transfer function H(z) is cascaded with a system to get a new system transfer function H2(z), try to compute the phase function and the group delay of .Solution:（共20分）(1) magnitude response:（共9分）(2) values of peaks in magnitude of :-/2,0,/2, , （2分） values of dips in magnitude of :,3/4, /4，/4, 3/4（2分）（3）The phase function ，The group delay（共7分）4.Using windowed Fourier series method, design a causal low-pass FIR digital filter with the following specifications: Pass band edges fp:6kHz Stop band edges fs:8kHz Pass band ripple p: 1dBStop band attenuations: 40dBSampling frequency FT: 20kHzSolution:（共15分） (1) Perform some specifications transform.（每个1分，共4分） (2) The ideal impulse response is（1分） (3) According the requirement of stop band attenuation, the Hann（or Hamming,Blackman） window should be chose. The transition bandwidth of hann window is 3.11/M, i.e., （2分） So, M = 16 and the Hann window function is（2分）(4) Windowing: htn = hLPnwn, -16 n 16（2分）Casual system: hn = htn -16, 0 n 33（2分）(5) Test：Compute H(ejw)=DTFT(hn) to verify.（1分） 5. The normalized transfer function of an order-2 low-pass Butterworth analog filter is as follows: .With bilinear transform, an order-2 low-pass IIR Butterworth digital filter with -3dB cutoff frequency at 1000Hz and sampling frequency at 4000Hz has been designed. The structure of the filter is sketched in figure 1. Determine the value of constant K and M and expression of prototype analog filter Ha(s).Solution:（共20分）（3分）Prewarp （2分）Prototype analog filter（5分）Bilinear transform6. In practice，digital filters are often used to process analog signal. The processing procedure is shown as figure 2, where T denotes sampling interval，and satisfies Nyquist Theorem. And we can regard it as an equivalent analog filter.y(t)Sampling based on ThnD/AIdeal Lowpass Filter with Cutoff Frequency beingx(t)Figure 2If the digital filter hn is a bandpass filter with the cutoff frequencies ，give the cutoff frequency and