数字信号处理A

1、浙江科技学院考试试卷 专业班级 学号 姓名 装订线 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)scorequestion 1 (8 marks)discrete-time s

2、ystem differential equation is given by where x(n) and y(n) are the systems 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 connec

3、tion 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(a) determine the nyquist frequency of(4 marks).(b) if is sampled at the double rate of the nyquist frequency, what is the sampling period ts o

4、f 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

5、lti discrete-time systems shown in the following structure, where, ,(a) determine the transfer function of the overall system as a ratio of two polynomials in (2 marks).(b) determine the difference equation characterizing the overall system (3 marks).(c) develop the realization of overall system wit

6、h 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 systems input and output.(a) determine the transfer functionand its region of convergence (roc) (3 marks).(b) determine th

7、e impulse response of the above system (3 marks).(c) if the system is a digital filter actually, is it an iir filter or fir filter? (2marks)question 8 (8 marks)let x(k), , be a 10-point dft of with first 5 samples of x(k) given by ，. a n-point dft property is well known, that is.（a）determine the oth

8、er 5 samples of x(k):（4 marks）.（b）determine by the formula of idft（4 marks）.part two applications (total 2 questions in this part, each question is marked out of 18 )score question 1（18 marks）design one low-pass iir digital filter h(z) with a sampling frequency of 4khz and digital filter requirement

9、s are specified by（1）the passband edge frequency ，the maximal passband attenuation .（2）the stopband edge frequency，the minuimum stopband attenuation.please refer to the following procedures for the design:（a） find the prewarp frequency andfor analog prototype filter design based on butterworth metho

10、d（6 marks）.（b） computer order n of butterworth prototype filter and its cutoff frequency （6 marks）.（c）determine the transfer functionfor butterworth filter (4 marks).（d）transform the analog transfer function to digital transfer function by bilinear transform method（2 marks）.following data and formul

11、as are provided for reference during your work. the denominator polynomial coefficients of butterworth prototype filter versus to various order nsna1a2a3a4a51121.414232.00002.000042.61313.41422.613153.23615.23615.23613.236163.86377.46419.14167.46413.8637，, where t is the sampling period.question 2（1

12、8 marks）to design a low-pass fir filter based on the sampling frequency 10 khz and its following requirements:(1) passband edge frequency, the maximal passband attenuation.(2) stopband edge frequency, the minimum stopband attenuation .following data and formulas are provided for reference during your work. relative sidelobe level /dbtransition bandwidthminimum stopb