数字信号处理08A.doc

浙江科技学院 2012-2013 学年第一学期考试试卷 A 卷 考试科目 数字信号处理 考试方式 闭 完成时限 2 小时 拟题人 审核人 批准人 2012 年 12 月 18 日 信息与电子工程 学院 2010 年级 电子信息工程（互联网方向）专业 题序 一 二 三 四 五 六 七 八 九 十 总分 加分人 复核人 得分 签名 Part one Fundamentals (Total 8 Questions in This Part, Each Question Is Marked out of 8) Score Question 1 (8 Marks) Discrete-time system differential equation is given by where x(n) and y(n) are the system’s input and output respectively, determine the linearity of the system. Question 2 (8 Marks) Determine the inverse z-transforms of the following z-transforms. (a), ROC （5 Marks） (b)（3 Marks）. Question 3 (8 Marks) Consider the connection of three LTI systems as follows，Let, and , then determine unit sample response of the whole system. Question 4 (8 Marks) Let the continuous-time signal is Determine the Nyquist frequency of(4 Marks). If is sampled at the double rate of the Nyquist frequency, what is the sampling period Ts of sine wave in the sampled sequence? What is the sampled signal? (4 Marks) Question 5 (8 Marks) Let x(n) be a length-3 sequence defined by (a) Determine the DTFT of x(n) (4 Marks). (b) Determine the N-point DFT of x(n) (4 Marks). 　 Question 6 (8 Marks) Consider the cascade of the three causal first-order LTI discrete-time systems shown in the following structure, where , , Determine the transfer function of the overall system as a ratio of two polynomials in (2 Marks). Determine the difference equation characterizing the overall system (3 Marks).. Develop the realization of overall system with each section realized in direct form I (3 Marks). Question 7 (8 Marks) The difference equation of a causal LTI discrete-time system is given by where the variables and represent system’s input and output. (a) Determine the transfer functionand its region of convergence (ROC) (3 Marks). (b) Determine the impulse response of the above system (3 Marks). (c) If the system is a digital filter a