数字信号处理 期末试题A.docVIP

《数字信号处理》课程试卷（A卷）课程代码：131300111 本试卷用于信息工程系2011级通信工程/电子科学与技术/电子信息专业本科学生（时量：120分钟 总分100分） 注意：1、答案必须填写在答题纸上，填写在试卷上无效 2、答卷必须写明题目序号，并按题号顺序答题 3、请保持行距，保持卷面整洁 (15 points) The impulse response and the input sequence of and LTI discrete system are denoted as, Determine the zero-state response . Let and be the 16-point DFT of and and Determine the sequence of . Plot the DFT-based implementation of determining and determine the point L of the DFT used in the DFT-based implementation. (15 points) Consider a sequence: , Determine DTFT of . Determine the 8-point DFT of using DIT-FFT approach. (10 points) Prove the Parseval’s Theorem: The total energy of a length-N sequence can be computed by summing the square of the absolute values of the DFT samples divided by N, that is (20 points) Using bilinear transformation method, design a high-pass IIR digital filter based on Butterworth or Elliptic analog filter. The specifications are, Pass-band edge frequency: 900Hz Maximum pass-band attenuation: 0.1dB Stop-band edge frequency: 600Hz Minimum stop-band attenuation: 60dB Spectral transformation: , where, denotes the Laplace transform variable of the prototype analog low-pass filter and the variable of the desired analog filter . (a) Give the main design steps. (b) Give the corresponding MATLAB program statements for each step. (20 points)Consider the following three IIR transfer functions of a causal digital filter, Are the transfer functions BIBO stable? What is the relation between their magnitude function? What is the relation between their phase function? Develop a canonic direct-form II realization for . (20 points)Suppose a FIR digital filter shown in Figure 1. Determine the transfer function H(z). Is it a linear-phase FIR filter and why? Determine the magnitude function and the phase function of the FIR digital filter. 第3页，共3页