山东大学2016-2017学年2学期数字信号处理（双语） 课程试卷(B) 号 三 四 五 七八 九 总分 阅卷人 A.absolutely stable; B.maybe stable and causal; C.absolutely causal; D.maybe stable but not causal 得分 Directions图 3)A Type II FIR Linear-Phase System can be used as a ). 好 1)The answers of this test should be in English. A.low-pass filter; B.low-pass or high-pass filter; 2)The full mark of this test is 100.The final course mark is based on this test (80%)and class C.high-pass filter; D.neither low-pass nor high-pass filter; record mark (20%). 3)Tables of properties of Discrete-time Fourier transform,z-transform and DFT are supplied to 4) Consider an L-point sequencexIn]and a P-point sequencex[n],for the circular you on the last page. 4)Unless otherwise indicated,answers must be derived or explained,not just simply written down. convolutionx n]x,In]and linear convolutionx[n]x,[n]to be identical,the circular convolution must have a length N of at least )points. 得分 卷人 (10 pts,2 pts for each)Choose the best answer to fill in the blanks. A.L+P41: B.L+P-1; C.L+P: D.L; 5)For a system H(z)that have the same magnitude response with the minimum-phase 1)If the poles of the system function H(z)ofa LTI system are as in the Figure,and the system Hmin(z),the correct description about H(z)is 茶 system is stable,then hin]is a 3 A.arg[H(e)]2argH()]:B.grd[H()]2h时： C. D. 得分厕卷人 2.(15 pts)Determine the z-transform of the following sequence, including the ROC(region of convergence).If the sequence is the impulse response hn]of an LTI system,is the system stable?Why? A.two-sided sequence (may be[n]=a'u[n]+'u[n]+c'u[-n-1]): n20 B.two-sided sequence (may be]='u[n]+c'u-n-1]): x(n)= n<0 器 C.right-sided sequence (may beun]): D.left-sided sequence (may be]=cu[-n-1]): 2)If the poles of a system function H(z)are all in the unit circle,then the system is 墨 第1页共4页
2016-2017 2 数字信号处理（双语） （B） 1 4 题号 一 二 三 四 五 六 七 八 九 十 总分 阅卷人 得分 Directions: 1) The answers of this test should be in English. 2) The full mark of this test is 100. The final course mark is based on this test (80%) and class record mark (20%). 3) Tables of properties of Discrete-time Fourier transform, z-transform and DFT are supplied to you on the last page. 4) Unless otherwise indicated, answers must be derived or explained, not just simply written down. 1．(10 pts, 2 pts for each) Choose the best answer to fill in the blanks. 1) If the poles of the system function H (z) of a LTI system are as in the Figure, and the system is stable, then h[n] is a ( ). A. two-sided sequence (may be ); B. two-sided sequence (may be ); C. right-sided sequence (may be ); D. left-sided sequence (may be ); 2) If the poles of a system function H (z) are all in the unit circle, then the system is ( ). A. absolutely stable; B. maybe stable and causal; C. absolutely causal; D. maybe stable but not causal 3) A Type II FIR Linear-Phase System can be used as a ( ). A. low-pass filter; B. low-pass or high-pass filter; C. high-pass filter; D. neither low-pass nor high-pass filter; 4) Consider an L-point sequence 1 x n[ ] and a P-point sequence 2 x n[ ] , for the circular convolution 1 x n[ ] ○N 2 x n[ ] and linear convolution 1 2 x n x n [ ]* [ ] to be identical, the circular convolution must have a length N of at least ( ) points. A. L+P+1; B. L+P-1; C. L+P; D. L; 5) For a system H(z) that have the same magnitude response with the minimum-phase system Hmin(z) , the correct description about H(z) is ( ). A. arg arg min ( ) ( ) jw jw H e H e ; B. ( ) min ( ) jw jw grd H e grd H e ; C. 2 2 min 0 0 n n m m h m h m = = ; D. 2 2 min 0 0 n n m m h m h m = = 2．(15 pts) Determine the z-transform of the following sequence, including the ROC (region of convergence). If the sequence is the impulse response h[n] of an LTI system, is the system stable? Why? 得分 阅卷人 得分 阅卷人 1 ( ) , 0 3 ( ) 1 ( ) , 0 2 − = − n n n x n n
山东大学2016-2017学年2学期数字信号处理（双语）课程试卷(B) 签 得分卷人 3.(10 pts)A discrete-time causal LTI system has the system function: (1+3z-4) H日)=1+0.52 Find expressions for a minimum-phase systemH()and an all-pass system H()such 家 that H()=H()H(). 游 海分圆卷人 5.(15 pts)The system function H(z)for an LTI system is as following. Find the impulse response hn],and draw the signal flow graph of parallel-form structure for the system. 1+2:+ H(日)=1-0.75+0.125. 器 将分侧卷人 4.(10 pts)Determine the group delay for0<<for the following sequences: 周 第2项共4页
2016-2017 2 数字信号处理（双语） （B） 2 4 3．(10 pts) A discrete-time causal LTI system has the system function: Find expressions for a minimum-phase system and an all-pass system such that . 4．(10 pts) Determine the group delay for 0 < ω < π for the following sequences: 5．(15 pts) The system function H(z) for an LTI system is as following. Find the impulse response h[n], and draw the signal flow graph of parallel-form structure for the system. 得分 阅卷人 得分 阅卷人 得分 阅卷人 ( ) min ( ) ( ) H z H z H z = ap H z min ( ) ( ) H z ap ( ) ( ) 1 1 1 3 . 1 0.5 z H z z − − + = + 1 1 1 2 2 n n x n − = + ( ) 1 2 1 2 1 2 1 0.75 0.125 − − − − + + = − + z z H z z z
山东大学2016-2017学年2学期数字信号处理（双语）课程试卷(B) 得分间卷人 6.(15 pts)Consider a causal continuous-time system with impulse response h(t)and system function()= 3x+2 Assume the sampling time is T=0.I s,use impulse invariance to determine H(z)for a discrete-time system such that hin]=The(nT). 签 家 得分圆卷人 8.(10 pts)Draw the signal flow graph for an 8-point decimation-in-time FFTalgorithm with bit-reversed ordering of the input time sequence x[n] and normal ordering of the output sequence X[k]. 得分 卷人 7.(15 pts)Compute the N-point circular convolution for the following sequences:xi(n)=1,-1,1,-11,x2(n)=(2,1,1,21, (a)N=4;(b)N=8;(c)Determine the minimum N when circular convolution equals to linear convolution. 器 第3项共4页
2016-2017 2 数字信号处理（双语） （B） 3 4 6． (15 pts) Consider a causal continuous-time system with impulse response hc(t) and system function 2 3 2 ( ) 2 3 1 c s H s s s + = + + . Assume the sampling time is T = 0.1 s, use impulse invariance to determine H(z) for a discrete-time system such that h[n]= Thc(nT). 7．(15 pts) Compute the N-point circular convolution for the following sequences: x1(n)={1,-1,1,-1}, x2(n)={2,1,1,2}, (a) N=4; (b) N=8; (c) Determine the minimum N when circular convolution equals to linear convolution. 8．(10 pts) Draw the signal flow graph for an 8-point decimation-in-time FFT algorithm with bit-reversed ordering of the input time sequence x[n] and normal ordering of the output sequence X[k]. 得分 阅卷人 得分 阅卷人 得分 阅卷人
山东大学2016-2017学年2学期数字信号处理（双语）课程试卷(B) TABLE 2.3 FOURIER TRANSFORM PAIRS TABLE 2.2 FOURIER TRANSFORM THEOREMS Sequence Fourier Transform Sequence Fourier Transform 1. 1 X(ej) 2.m-o】 e-jono 好 y Y(el) 1.ax(n]+byin] ax(el)+bY(el) 3.1(-o0n←0∞) ∑e+2x的 2.x(n-ndl (n an integer) e-junX(ejo) 4.an(al1 游 3.-d-n- 1-x可 10) TABLE8.2 or oo (if m<0) Properties of the DFT 5.a"uln] 1-a可 la lal Finite-Length Sequence(Length N) N-point DFT (Length N) 6.-ad-n-1] la<lal 1.x(n] XI周 2.x[n].x2ln] X:[).X2[k] TABLE 3.2 SOME z-TRANSFORM PROPERTIES 的 3.ax[n]+bx2in] aX因+bXl附 Section Reference Sequence Transform ROC 4.X Nx[((-k))N] xin] X(2) Rr 5.x[((n-m))N] WmX[内 a X R 6.Wyx[n] X(-)》N X2(z) Rn N 3.41 网+br aX(z)+bx2(z) Contains R:nR X内X2R 3.42 x[n -no] 刷X() R.except for the possible 器 ∑n(mxI(n-mjN m=0 addition or deletion of N-1 the origin oroo 8.x[n]x2In] x()x2((k-6)N] 3.43 网 X(z/zo) lzoRr 3.4.4 网 Rr.except for the possible 墨 addition or deletion of the origin or oo 第4页共4页
2016-2017 2 数字信号处理（双语） （B） 4 4 Properties of the DFT