山东大学 2011-2012学年2学期数字信号处理（双语）课程试卷(B) 号 三 四 七 八九 总分 阅卷人 A.low-pass filter, B.low-pass or high-pass filter, 得分 C.high-pass filter, D.neither low-pass nor high-pass filter; Directions图 得分 卷人 2.(15 pts)For the system T(x[n])=g[nb[n]with gin]given 架 1)The answers of this test should be in English. and bounded,determine whether the system is (1)stable,(2)causal,(3) 2)The full mark of this test is 100.The final course mark is based on this test (80%)and class linear,(4)time invariant,and(5)memoryless. 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. 得分 卷人 1. (10 pts,2 pts for each)Choose the best answer to fill in the blanks. 的 1)For a system for which the input and output satisfy a linear constant-coefficient difference 游 equation,if the system is initially at rest,then the system: A.is definitely not LTI system;B.may not be LTI; C.must be LTI but noncausal:D.must be LTI and causal: 2)Ifa LTI system is causal,then its impulse response h[n]is a( A two-sided sequence;B.a right-sided sequence,and maybe h[n]0,for n0;D.right-sided sequence,and hin]=0,for n<0; 的 : 3)Consider an L-point sequencex[n]and a P-point sequencexn],for the circular 得分 卷人 3.(10 pts)The difference equation relating x[n]and y[n]of a causal LTI system is as following:ynl +0.1un-1]-0.06 yin-2]xn)-2xIn-11. convolution xInx,In]and linear convolutionxIn*x,In]to be identical,the circular 1)Determine the system function H and the ROC. convolution must have a length N of at least )points. 2)Plot the poles and zeros of the system function in the z-plane. A.L+P+1; B.L+P-1; C.L+P; D.L; 怨 4)The inverse of a minimum-phase system is 人 A.absolutely stable and causal; B.may not be stable and causal; D.maybe stable but not causal 暴 C.maybe causal but not stable; 5)A Type IV FIR Linear-Phase System can be used as a( 第1负共4页
2011-2012 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) For a system for which the input and output satisfy a linear constant-coefficient difference equation, if the system is initially at rest, then the system: A. is definitely not LTI system; B. may not be LTI; C. must be LTI but noncausal; D. must be LTI and causal; 2) If a LTI system is causal, then its impulse response h[n] is a ( ). A two-sided sequence; B. a right-sided sequence, and maybe h[n] ǂ0, for n0; D. right-sided sequence, and h[n]=0, for n<0; 3) 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; 4) The inverse of a minimum-phase system is ( ). A. absolutely stable and causal; B. may not be stable and causal; C. maybe causal but not stable; D. maybe stable but not causal 5) A Type IV 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; 2．(15 pts) For the system T x n g n x n ( [ ]) [ ] [ ] = with g[n] given and bounded, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, and (5) memoryless. 3．(10 pts) The difference equation relating x[n] and y[n] of a causal LTI system is as following:y[n] + 0.1y[n-1]- 0.06 y[n-2] = x[n] - 2x[n-1]. 1) Determine the system function H(z) and the ROC. 2) Plot the poles and zeros of the system function in the z-plane. 得分 阅卷人 得分 阅卷人 得分 阅卷人
山东大学 2011-2012学年2学期数字信号处理（双语）课程试卷(B) 得分港人 4.(15 pts)We wish to design an FIR lowpass filter satisfying the 得分 港人 5.(10 pts)The following figure shows the impulse response for a specifications 0.95sH(es1.05s0.25e FIR LTI linear-phase system. H(e)s0.1,0.35sls by applying a window w/n/to the impulse response h/n/for the ideal discrete-time lowpass 好 012345678 filter with cutoff oe=0.3z.(given log 0.05=-1.3 (a)Which of the windows listed in the table can be used to meet this specification?(6 pts) 1)Determine the group delay associated with the system.(5 pts) (b)For each window that you claim will satisfy this specification,give the minimum length 2)It is known that there are four types of FIR linear-phase systems,so determine which M+I required for the filter.(9 pts) type of FIR linear-phase system the above system is.(5 pts) Peak Approximation Approximate Error, Type of Width of 20log108 Window Main Lobe (dB) 都 Rectangular 4/(M+1) -21 Bartlett 8n/M -25 Hanning 8x/M -44 Hamming 87/M -53 Blackman 12a/M -74 器 得分卷人 6.(15 pts)The system function of a LTI system is 2.870.18-2.35-2 He)=-0-03-X0-0.6e5 (a)Determine the difference equation relating x[n]and y[n].(7pts) 爱 (b)Draw the signal flow graph of cascade structure of the system with Ist-order sections (8 pts) 第2页共4页
2011-2012 2 数字信号处理（双语） （B） 2 4 4．(15 pts) We wish to design an FIR lowpass filter satisfying the specifications by applying a window w[n] to the impulse response hd [n] for the ideal discrete-time lowpass filter with cutoff ωc = 0.3π. (given ) (a) Which of the windows listed in the table can be used to meet this specification? （6 pts） (b) For each window that you claim will satisfy this specification, give the minimum length M + 1 required for the filter. （9 pts） 5．(10 pts) The following figure shows the impulse response for a FIR LTI linear-phase system. 1) Determine the group delay associated with the system. （5 pts） 2) It is known that there are four types of FIR linear-phase systems, so determine which type of FIR linear-phase system the above system is. （5 pts） 6．(15 pts) The system function of a LTI system is 1 1 1 1 1 2.87(1.18 )(2.35 ) ( ) (1 )(1 0.3 )(1 0.6 ) z z H z z z z − − − − − − − = − − − (a) Determine the difference equation relating x[n] and y[n]. （7pts） (b) Draw the signal flow graph of cascade structure of the system with 1st-order sections. （8 pts） 得分 阅卷人 得分 阅卷人 得分 阅卷人 ( ) ( ) 0.95 1.05, 0.25 0.1, 0.35 jw jw H e w H e w 10 log 0.05 1.3 = −
山东大学2011-2012学年2学期数字信号处理（双语）课程试卷(B) 签 将分侧卷人 8.(10 pts)Draw the flow graph for an 8-point decimation-in-frequency FFT algorithm with normal ordering of the input time sequence xn]and bit-reversed ordering of the output sequence X[k]. 家 得分侧卷人 7.(15 pts)Two same sequences xi[n]and xa[n]are as following: x[川，x川 0 (a)Determine 5-point DFTXi[k]of the sequence xi[n].(7 pts) (b)Determine the 10-point circular convolution x3 [n]=x[n]10x2n].(8 pts) 器 第3项共4页
2011-2012 2 数字信号处理（双语） （B） 3 4 7．(15 pts) Two same sequences x1[n] and x2[n] are as following: (a) Determine 5-point DFT X1[k] of the sequence x1[n]. （7 pts） (b) Determine the 10-point circular convolution x3 [n] = x1[n]○10 x2[n]. （8 pts） 8．(10 pts) Draw the flow graph for an 8-point decimation-in-frequency FFT algorithm with normal ordering of the input time sequence x[n] and bit-reversed ordering of the output sequence X[k]. 得分 阅卷人 得分 阅卷人 1 2 x n x n [ ], [ ]
山东大学2011-2012学年2学期数字信号处理（双语）课程试卷(B) TABLE 2.2 FOURIER TRANSFORM THEOREMS TABLE 2.3 FOURIER TRANSFORM PAIRS Sequence Fourier Transform Sequence Fourier Transform xn X(e) 1 y Y(ei) 1. 2.m-o】 e-jono 好 1.ax[n]+byn] ax(el)+bY(ei) 3.1(-o0n←0∞) 2.x[n-na](na an integer) e-junX(eiw) +2a k一x 3.ejoonx[n] X(ef-wo)) 4.an(al1 游 3.-4-n- 1-x可 10) or oo (if m<0) Finite-Length Sequence(Length N) N-point DFT(Length N) 5.a"uln] 1-a可 la lal 1.x(n] XI内 6.-ad-n-1] la<lal 2.xiln].x2ln] X:[).X2[] TABLE 3.2 SOME z-TRANSFORM PROPERTIES 的 3.ax[n]+bx2in] aX内+bX周 4.X[n] Section Nx[((-k))N] Reference Sequence Transform ROC 5.x[((n-m))N] w装mX xin] X(2) R: 6. Wnxinl X(k-)》N a X R N- ∑mala-m al X2(z) Rn 7. X肉X2肉 3.41 网+br aX(z)+bx2(z) Contains R:nR 3.42 x[n -no] :X( R.except for the possible 器 addition or deletion of 8.xIn]x2In] X1()X2(k-)N the origin or oo 3.43 网 X(z/zo) lzoRr 3.4.4 网 Rr.except for the possible addition or deletion of the origin or oo 第4页共4页
2011-2012 2 数字信号处理（双语） （B） 4 4 Properties of the DFT