南京理工大学课程考试试卷(学生考试用 )

1、南京理工大学课程考试试卷(学生考试用 )课程教学大纲编号：04027704课程名称：Digital Signal Processing 学分：3.5试卷编号：001考试方式：闭卷笔试考试时间：120分钟满分分值：100分组卷年月： 组卷教师：审定教师：学生班级:学生学号: 学生姓名:Notice!1. All the answers should be written in the answer sheet!2. The following may be used for your answers: (1) Properties of common window functions: Rect

2、angularBartlettHanningHammingBlackmanWidth of mainlobe4/(M+1)8/M8/M8/M12/MPeak approximation error (dB)-21-25-44-53-74(2) Kaiser window: 1. Basic concepts: (18% )(1) Find the impulse response hn and the frequency response H(e jw)of the overall system shown in Fig 1.Figure 1(2) The system is shown in

3、 Fig.2, in which H(z) = (1-0.8 e j 0.3p z-1)( 1-0.8 e- j 0. 3p z-1)(1-1.2 e j 0.7p z-1)( 1-1.2 e- j 0.7p z-1)Figure 2Find a stable and causal Hc(z) =so that the magnitude of the overall system |G(e jw)| =1.(3) The phase spectrum of sequence xn = dn + 2dn -1 +dn -2 is j(w) = .(4) Suppose xn Xk (0 n N

4、 -1, 0 k N -1), then WN 2kXk.(5) A finite-length sequence xn.is shown in Fig.3. Sketch the sequences x1n and x2n specified as:x1n= x(n2)4 ,0 n 3,x2n= x(n)4,0 n 3Figure 32. (10%) A causal LTI system is described by the following difference equation： (1) Determine the impulse response hn of the system

5、.(2) Determine the step response gn of the system.3. (8%) In Fig.4, xn = x c( nT ) and yn = x2n .(1) If x c (t) has a Fourier transform such that X c ( jW) = 0, |W| 2p100, what value of T is required so that X (e jw) = 0, p/21/4, , -5分 注：该题为综合题，考核逆系统、最小相位系统及系统补偿等知识点。 5. Hanning Window, M = 65-4分 注：该

6、题为基本题，考核FIR系统设计中的相关参数选择等知识点。 6. -4分 注：该题为基本题，考核IIR系统实现中的有限字长效应等知识点。 II. ( 35分 )Computation1. -4分 -2分 注：该题为基本题，考核DFT的计算等知识点。 2. -8分 注：该题为基本题，考核圆周卷积的计算等知识点。 3. (i)f smin = 4000Hz;-3分 (ii) N= f smin/F=4000/2.5=1600For radix-2 FFT,let N=2048., tp=NT=N/ f smin=512ms-3分 注：该题为提高题，考核应用DFT分析连续时间信号频谱分析的有关参数等知

7、识点。 4. -5分 注：该题为基本题，考核逆z变换等知识点。 5. -2分 -2分 -2分 -2分 14344()-2分 注：该题为基本题，考核有关DFT的数值计算等知识点。 III.Analysis and design: ( 40分 )1(i)ROC:-3分 (ii) -3分 (iii) It is not a stable system.-3分 注：该题为基本题，考核离散时间系统差分方程的分析等知识点。 2.（i）-4分 -2分 注：该题为基本题，考核IIR系统地双线性变换设计等知识点。 3（i） So it is a generalized linear phase system.-

8、4分 （ii）-3分 （iii）When , -2分 注：该题为基本题，考核线性相位FIR系统的性质及结构等知识点。 4(i)Let , Using N-point FFT , Using the symmetric property of DFT,And,for -4分 (ii)Complex multiplications: Complex additions: -2分 (iii) -10分 注：该题为基本题，考核有关FFT算法结构及相关参数等知识点。南京理工大学课程考试参考答案及评分标准课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：001I.（25）

9、Basic concepts:1,- 4 point注：该题为基本题，考核DFT的基本性质等知识点 2. Continuous, AperiodicContinuous, Periodic;Periodic，Discrete- 6 point注：该题为基本题，考核傅里叶变换的周期性与连续性的关系等知识点 3. 500p,3500p- 2 point注：该题为综合题，考核连续信号的取样及频谱混叠等知识点 4. （6） ROC:|z|0.5, , - 6 point注：该题为基本题，考核逆系统及最小相位系统等知识点 5. Hamming Window, M=48- 4 point注：该题为基本题，

10、考核窗函数法设计FIR数字滤波器等知识点 6. - 3 point注：该题为基本题，考核数字系统实现中有限字长效应等知识点 II. ( 35 )Computation1. - 6 point注：该题为基本题，考核DFT的计算等知识点 2. - 8 point注：该题为基本题，考核圆周卷积与线性卷积等知识点 3. (i)f smin = 2000Hz; (ii) F = f smin/ NF=2000/1024=1.953125Hz- 6 point注：该题为综合题，考核连续信号的取样、时域分辨率及频谱分辨率等知识点 4. - 5 point注：该题为基本题，考核z变换及其逆变换计算等知识点 5

11、. =- 10point注：该题为提高题，考核DFT及其有关性质的应用等知识点III.Analysis and design: ( 40 )1(i)- 3pointROC:- 2point(ii) - 2point(iii) It is not a stable system.- 2point注：该题为基本题，考核离散系统的因果性及其稳定性等知识点 2. - 4point - 2point注：该题为综合题，考核IIR数字滤波器的设计及其频响特性等知识点 3(i) - 3point (ii) So it is a generalized linear phase system.- 4point（

12、iii）When , - 2point注：该题为综合题，考核系统的连接方式及线性相位数字滤波器等知识点 4(i) Let Using N-point FFT , Using the symmetric property of DFT,- 4point(ii) Complex multiplications: Complex additions: - 2point (iii) - 10point注：该题为基本题，考核DFT的计算及其快速算法FFT等知识点 南京理工大学课程考试参考答案及评分标准课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：001I.（25）B

13、asic concepts:1,- 4 point注：该题为基本题，考核DFT的基本性质等知识点 2. Continuous, AperiodicContinuous, Periodic;Periodic，Discrete- 6 point注：该题为基本题，考核傅里叶变换的周期性与连续性的关系等知识点 3. 500p,3500p- 2 point注：该题为综合题，考核连续信号的取样及频谱混叠等知识点 4. （6） ROC:|z|0.5, , - 6 point注：该题为基本题，考核逆系统及最小相位系统等知识点 5. Hamming Window, M=48- 4 point注：该题为基本题，考

14、核窗函数法设计FIR数字滤波器等知识点 6. - 3 point注：该题为基本题，考核数字系统实现中有限字长效应等知识点 II. ( 35 )Computation1. - 6 point注：该题为基本题，考核DFT的计算等知识点 2. - 8 point注：该题为基本题，考核圆周卷积与线性卷积等知识点 3. (i)f smin = 2000Hz; (ii) F = f smin/ NF=2000/1024=1.953125Hz- 6 point注：该题为综合题，考核连续信号的取样、时域分辨率及频谱分辨率等知识点 4. - 5 point注：该题为基本题，考核z变换及其逆变换计算等知识点 5.

15、 =- 10point注：该题为提高题，考核DFT及其有关性质的应用等知识点III.Analysis and design: ( 40 )1(i)- 3pointROC:- 2point(ii) - 2point(iii) It is not a stable system.- 2point注：该题为基本题，考核离散系统的因果性及其稳定性等知识点 2. - 4point - 2point注：该题为综合题，考核IIR数字滤波器的设计及其频响特性等知识点 3(i) - 3point (ii) So it is a generalized linear phase system.- 4point（i

16、ii）When , - 2point注：该题为综合题，考核系统的连接方式及线性相位数字滤波器等知识点 4(i) Let Using N-point FFT , Using the symmetric property of DFT,- 4point(ii) Complex multiplications: Complex additions: - 2point (iii) - 10point注：该题为基本题，考核DFT的计算及其快速算法FFT等知识点 南京理工大学课程考试试卷 ( 学生考试用 )课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：001考试方式：

17、闭卷笔试考试时间：120分钟满分分值：100分组卷年月：组卷教师：审定教师：Notice!1. All the answers should be written in the answer sheet!2. The following may be used for your answers: (1) Properties of common window functions: RectangularHanningHammingBlackmanBandwidth of transition1.84/N6.22/N6.64/N11.2/NMinimum stopband attenuation

18、 (dB)-21-44-55-75(2) Kaiser window: 3. Some useful equations: 4. Some useful signs: - modular operation; - N-point circular convolution *- convolution sumI. Basic concepts: ( 30 )1. Which kind of signal has a continuous and period frequency spectrum. 2. Consider the sequence for .Find the conjugate

19、symmetric part ；and the conjugate antisymmetric part 。3. Let , Find the DFTs of following sequences: , , , 4. Let . Find the inverse z transform .5. Let the sequence , and its 8-point DFT is Xk, 0 k 7, please fill the following blanks:（a）；（b）； （c）；（d）。 6. A 2nd-order causal and stable allpass system

20、 with real impulse response has one pole at. Find its transfer function , and its ROC is .7. To compute the N-point DFT of a sequence xn (0 n N-1)directly by the DFT analysis equation, how many complex multiplications are needed:. If using a radix-2 FFT algorithm, how many complex multiplications ar

21、e needed:.II. Computation: ( 30 )1. (6) Compute the 4-ponit DFT Xk of a sequence, xn =3,2,0,2.2. (8) Let xn = 1, -2, 0, 2,0 n 3, and hn= 2, -1, 1, -2,0 n 3. Determine: (1) yn=xn * hn;(2) wn=xn hn.3.(8) A causal LTI system is described by the following difference equation:(1) Determine the impulse re

22、sponse hn of this system;(2) If the input sequence is xn =, determine the output sequence yn.4.(8) Consider a length- N sequence xn, 0 n N -1, with an N-point DFT Xk, 0 k N -1, where N is an even number. (1) Let sequence , determine the N-point DFT Yk, 0 k N -1;(2) Let sequence , 0 n N -1. Determine

23、 the N-point DFT Wk, 0 k N -1;(3) Let sequence, 0 n N /2-1, determine the N/2-point DFT Zk, 0 k N/2 -1.III. Analysis and design: ( 40 )1. （8）A causal IIR LTI discrete-time system is characterized by the input-output relation:(1) Determine the system function H(z) ;(2) Sketch the magnitude response |

24、H(e jw)|and phase responsej (w).2. (9) A causal LTI discrete-time system is characterized by system function:(1) Determine the impulse response hn of this system;(2) Prove that the system has a linear phase response;(3) Plot the linear phase structure flowgraph to realize this system.3. (10) (1) A c

25、ausal analog system function is , Design a corresponding digital filter by bilinear transform method ( assume T=2), determine the digital system function H(z);(2) Design a highpass FIR filter with the smallest length using the window-based approach and meeting the specifications:Select a suitable wi

26、ndow function wn, determine the filter length N and impulse response hn.4. (13) Use DIT-FFT algorithm to compute the N-point DFT Xk, 0 k N -1, of a length-N sequence xn, 0 n N -1, where N = 2m. (1) When N = 8, plot one class of butterfly flow graph of the algorithm;(2) When N = 512, Determine the co

27、efficients of the 5th-stage. 南京理工大学课程考试试卷 ( 学生考试用 )课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：002考试方式：闭卷笔试考试时间：120分钟满分分值：100分组卷年月：组卷教师：审定教师：Notice!1. All the answers should be written in the answer sheet!2. The following may be used for your answers: (1) Properties of common window functions: Rectang

28、ularHanningHammingBlackmanBandwidth of transition1.84/N6.22/N6.64/N11.2/NMinimum stopband attenuation (dB)-21-44-55-75(2) Kaiser window: 3. Some useful equations: 4. Some useful signs: - modular operation; - N-point circular convolution*- convolution sumI. Basic concepts: ( 30 )1. Let , then , .,2.

29、Fill the blanks according to the rules you observed:Time DomainFrequency DomainPeriodic, ContinuousDiscrete, AperiodicContinuous, AperiodicAperiodic, DiscretePeriodic Discrete3. Let . The inverse z transform of is.4. Consider the sequence, defined for , Find the 6-point circular conjugate symmetric

30、sequence ；and the circular conjugate antisymmetric sequence 。 5. Let the sequence , and its 8-point DFT is Xk, 0 k 7, please fill the following blanks:（a）；（b）； （c）；（d）。 6. To compute the 512-point DFT of a sequence xn (0 n 511) directly by the DFT analysis equation, how many complex multiplications

31、are needed:. If using a radix-2 FFT algorithm, how many complex multiplications are needed:.7. An FIR system has impulse response, its zeros are:, it is a (lowpass, highpass, etc) filter.8. An causal system has transfer function, it is (stable, or unstable), and its impulse response.II. Computation:

32、 ( 30 )1.(6) Compute the 4-ponit DFT Xk of sequence xn=1,2,0,4.2.(8) Assume xn=2n,0 n 3, hn=1+(-1)n,0 n 3, determine:(1) yn=xn * hn;(2) wn=xn hn. 3.(4) An analog signal x(t) with its Fourier transform X(jW) satisfies X(jW) = 0 for |W| 3 2p(1000)xn is the sampled sequence with Nyquist rate, and Xk is

33、 1024-point DFT of xn.(1) Determine the Nyquist rate f smin； (2) Determine the frequency spacing between spectral samples.3.(8) A causal LTI system is described by the following difference equation:(1) Determine the impulse response hn of this system;(2) If the input sequence is xn =, determine the

34、output sequence yn.4.(4) Consider a length- N sequence xn, 0 n N -1, with an N-point DFT Xk, 0 k N -1, where N is an even number. (1) Let sequence , determine the N-point DFT Zk, 0 k N -1;(2) Let sequence, 0 n N -1. Determine the N-point DFT Yk, 0 k N -1;III. Analysis and design: ( 40 ) 1. （8）A caus

35、al LTI system is described by the difference equation(1) Find the system function H(z) for this system. Plot the poles and zeros of H(z) and indicate the ROC;(2) Draw the signal flow graph2. (6) There is an analog filter with the system function , Design a corresponding digital filter by bilinear tr

36、ansform respectively( assume T=2)(1) Find the digital system function H(z);(2) Sketch the magnitude response of the designed digital filter.3. (8) Assume h1n=1,2,2,1 and h2n=2, 1,0, -1, -2 in the following figure.(1) Determine the impulse response of the overall system.(2) Show that the overall syst

37、em is a linear phase system, and plot the linear-phase structure flow graph.4. (18) Use DIT-FFT algorithm to compute the N-point DFT Xk, 0 k N -1, of a length-N sequence xn, 0 n N -1, where N = 2m. (1) When N = 8, plot one class of butterfly flow graph of the algorithm;(2) When N = 256, Determine th

38、e coefficients of the 5th-stage. (3) Use the above FFT for 512-point DFT once to compute the DFT of length-1024 real sequence. Draw the block diagram of the realization. 南京理工大学课程考试参考答案及评分标准课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：01I.（30分）Basic concepts: 1. Aperiodic and discrete signal-2分注：该题为基本题，

39、考核信号的时间波形及其频谱特征之间的关系等知识点。 2. -4分 注：该题为基本题，考核有限长序列的共轭对称分量和共轭反对称分量等知识点。 3. ,，-6分 注：该题为综合题，考核DFT的性质及应用等知识点。 4. -2分 注：该题为基本题，考核z变换及其逆变换的求解等知识点。 5. （a）11；（b）-9；（c）16；（d）440-8分 注：该题为基本题，考核DFT有关参数的计算等知识点。 6. , -4分 注：该题为综合题，考核全通滤波器的系统函数特点等知识点。 7. ；-4分 注：该题为基本题，考核DFT有关参数的计算等知识点。 II. ( 30分 )Computation1. -4分

40、-2分 注：该题为基本题，考核DFT的计算等知识点。 2. -4分 -4分 注：该题为基本题，考核线性卷积和圆周卷积的计算等知识点。 3. -6分 -2分 注：该题为基本题，考核线性时不变离散时间系统差分方程的求解等知识点。 4. （1） -3分 （2） -3分 （3） -2分 注：该题为提高题，考核DFT的综合应用等知识点。 III. Analysis and design: ( 40分 )1. (1) , (2)-4分 -4分 注：该题为基本题，考核离散时间系统差分方程的分析和频率响应等知识点。2.（1）-3分 （2）So it is a generalized linear phase

41、system.-3分 （3）-3分 注：该题为基本题，考核线性相位FIR系统的性质及结构等知识点。 3. （1）-5分 （2）Select Hanning window-3分 -2分 注：该题为基本题，考核IIR和FIR数字滤波器的设计等知识点。 4. -10分 （2）-3分 注：该题为基本题，考核有关FFT算法结构及相关参数等知识点。南京理工大学课程考试参考答案及评分标准课程教学大纲编号：04027704课程名称：数字信号处理（英）学分：3.5试卷编号：01I.（30分）Basic concepts:1. , ，-6分 注：该题为综合题，考核DFT的性质及应用等知识点。 2. Aperiod

42、ic and Continuous signalPeriodic and Continuous signalPeriodic and discrete signal-6分注：该题为基本题，考核信号的时间波形及其频谱特征之间的关系等知识点。3. -2分 注：该题为基本题，考核z变换及其逆变换的求解等知识点。 4. -4分 注：该题为基本题，考核有限长序列的共轭对称分量和共轭反对称分量等知识点。 5. （a）5.3；（b）5.3；（c）18.4；（d）470.32-4分 注：该题为基本题，考核DFT有关参数的计算等知识点。 6. ；-2分 注：该题为基本题，考核DFT有关参数的计算等知识点。 7.

43、 0，Bandpass-2分 注：该题为综合题，考核FIR线性相位滤波器的零点分布及滤波特点等知识点。 8. Stable, -4分 注：该题为综合题，考核系统的因果性与系统函数的关系等知识点 II. ( 30分 )Computation1. -4分 -2分 注：该题为基本题，考核DFT的计算等知识点。 2. -4分 -4分 注：该题为基本题，考核线性卷积和圆周卷积的计算等知识点。 3. -2分 -2分 注：该题为综合题，考核信号频谱分析的相关参数等知识点。 4. -6分 -2分 注：该题为基本题，考核线性时不变离散时间系统差分方程的求解等知识点。 5. （1）-2分 （2）-2分 注：该题为

44、提高题，考核DFT的综合应用等知识点。III. Analysis and design: (40分)1. (1) ,，Poles: ,zero: z=0-4分 (2) 图略-4分 注：该题为基本题，考核离散时间系统差分方程的分析和频率响应等知识点。 2. （1）-4分 （2）图略-2分 注：该题为基本题，考核IIR数字滤波器的设计等知识点。 3. （1）-5分 （2），图略-3分 注：该题为基本题，考核线性相位FIR系统的性质及结构等知识点。 4 -12分 （2）-2分 注：该题为基本题，考核有关FFT算法结构及相关参数等知识点。 （3）图略-4分 课程教学大纲编号：04027704课程名称：

45、数字信号处理（英）学分：3.5试卷编号：012考试方式：闭卷笔试考试时间：120分钟满分分值：100分组卷年月：组卷教师：审定教师：学生班级：学生学号: 学生姓名:Notice!1. All the answers should be written in the answer sheet!2. The following may be used for your answers: (1) Properties of common window functions: RectangularBartlettHanningHammingBlackmanWidth of mainlobe4/(M+1

46、)8/M8/M8/M12/MPeak approximation error (dB)-21-25-44-53-74(2) Kaiser window: I. Basic concepts: ( 35 )1. An IIR digital highpass filter is to be designed by transforming an analog highpass filter with the cutoff frequency fp at 0.5kHz using the bilinear transform method with T=0.2ms. The normalized

47、cutoff frequency of the digital filter is wp =.2. Fill in the blank according to the relations of the periodicity and discreteness of a signal in time-domain and frequency-domain:3. Consider the following length-8 sequences defined for 0n7:(a) x1n=1, 1, 1, 0, 0, 0, 1, 1,(b) x2n=1, 1, 0, 0, 0, 0, -1,

48、 -1,(c) x3n=0, 1, 1, 0, 0, 0, -1, -1,(d) x4n=0, 1, 1, 0, 0, 0, 1, 1,Which sequences have a real-valued 8-point DFT? Which sequences have an imaginary-valued 8-ponit DFT? Why?4. The system function of a causal and stable linear time-invariant system is given by . Please determine whether this system

49、is a minimum-phase system and also determine whether the inverse system is causal and stable5. If we want to design an FIR lowpass digital filter, and the specification is: (1) the attenuation of the stopband should more than 30dB, (2) the bandwidth of the transition band should be less than p/8. Pl

50、ease select a suitable window function and determine the smallest length of the window (M).6. There are two discrete-time systems with the system functions as below: and , Please determine which system is more sensitive to the coefficients quantization, and show the reason.II. Computation: ( 25 )1.

51、Suppose sequence xn=1, 1, 1, 1, Compute its DTFT: X(ejw)., and sketch its magnitude curve | X(ejw) | and angular curve arg X(ejw) . 2. Assume the system with function is implemented using (B+1)-bit fixed-point arithmetic in all the computations and all products are rounded to (B+1) bits before additions are performed. Draw linear noise model of the system in direct form I.3. Evaluate the following functions of Xk where Xk (0 k 7) is the 8-point DFT of the sequence : xn=3,-1,2,4,-3,-2,0,1, (0 n 7).(a) X0,(b