山东大学 2018-2019学年2学期数字信号处理（双语）课程试卷(A) 得分港人 3.(15pts)The impulse response hin]for a Linear-Phase FIR system is 得分 侧港人 4.(20 pts)For an ideal discrete-time differentiator with linear phase,the shown in the following figure, frequency response is Hn(e)=(jo)emn,-π<o<π An FIR discrete-time differentiatorn is determined byh[w],wn]is a symmetric window of length(M+1). (a)Determine the system function. (a)Find the corresponding impulse responseof H(). (b)Determine the difference equation relating input x[n]and output y[n] (b)Prove the symmetry or anti-symmetry ofh([Mor (c)Draw the signal flow graph of direct form structure for the FIR linear-phase system with the smallest number of coefficient multipliers. h[M-n=-hr[可y (d)Determine the group delay of the system. (c)Prove the symmetry or anti-symmetry ofn](h[n]=h[M-n]or h[M-n]=-h[n]). (d)If M9,which type of FIR generalized linear-phase system theis? (e)If M=10,which type of FIR generalized linear-phase system theis? (f)Choose an appropriate M (between M=10 and M=9)for the FIR discrete-time 家 differentiator,and give the reason. 琴 第2项共5页2018-2019 2 数字信号处理（双语） （A） 2 5 3．(15pts) The impulse response h[n] for a Linear-Phase FIR system is shown in the following figure, (a) Determine the system function. (b) Determine the difference equation relating input x[n] and output y[n]. (c) Draw the signal flow graph of direct form structure for the FIR linear-phase system with the smallest number of coefficient multipliers. (d) Determine the group delay of the system. 4．(20 pts) For an ideal discrete-time differentiator with linear phase, the frequency response is ( ) / 2 ( ) , . − = −   j j M H e j e diff       An FIR discrete-time differentiator h n  is determined by h n h n w n  = diff     , w[n] is a symmetric window of length (M +1). (a) Find the corresponding impulse response h n diff   of ( ) j H e diff  . (b)Prove the symmetry or anti-symmetry of h n diff   ( h M n h n diff diff  − =   or h M n h n diff diff  − − =   ). (c) Prove the symmetry or anti-symmetry of h n  ( h[n]= h[M – n] or h[M – n] = -h[n]). (d)If M=9, which type of FIR generalized linear-phase system the h n  is? (e) If M=10, which type of FIR generalized linear-phase system the h n  is? (f) Choose an appropriate M (between M=10 and M=9) for the FIR discrete-time differentiator, and give the reason. 得分 阅卷人 得分 阅卷人