數(shù)字信號(hào)處理試題

1、Test Of Digital Signal Processing 1Give the answer of the following problems as possible in English.1. Supposing when and .Please give its ZT , DTFTand N-point DFT .Explain the relations among these three transforms .2.A real 8-point sequence .Its 8-point DFT is Xk.(1) Supposing.Sketch .(2) Determin

2、e the value of . 3. A sequence has the 128-point DFT. Give the expression of . 4. A causal LTI discrete-time system has the transfer function .(1) Determine the difference equation of the system.(2) Give the pole-zero plot and the ROC of the system.(3) Is this system stable?(4) Develop a realization

3、 of the system in any canonic form.5. Design a FIR linear phase causal LPF which has cutoff frequency , transition bandwidth and minimum stopband attenuation .Develop the impulse response in closed form by Windowed Fourier Series method.6.If you use following MATLAB program to design a lowpass filte

4、r ,which has the specifications:passband edge 800Hz ,stopband edge 1kHz, passband ripple 0.5dB, minimun stopband attenuation 40dB ,and sampling rate is 5kHz.What data should you input to the computer?% Program For Elliptic IIR Lowpass Filter Design%Wp = input(Normalized passband edge = );Ws = input(

5、Normalized stopband edge = );Rp = input(Passband ripple in dB = );Rs = input(Minimum stopband attenuation in dB = );N,Wn = ellipord(Wp,Ws,Rp,Rs)b,a = ellip(N,Wn);h,omega = freqz(b,a,256);plot (omega/pi,20*log10(abs(h);grid;xlabel(omega/pi); ylabel(Gain, dB);title(IIR Elliptic Lowpass Filter);7. In t

6、he system of Figure (a), has a bandlimited spectrum as sketched in Figure (b) and is being sampled at the Nyquist rate. The digital ideal LPF has the frequency response as shown in Figure (c) .Sketch the spectrum ,and of ,and respectively.Test Of Digital Signal Processing2Give the answer of the foll

7、owing problems in English as possible as you can.1. Determine the fundamental period of sequence .2. Consider the z - transform .(1) (1) Give the pole-zero plot of .(2) (2) Determine all possible ROCs of . Discuss the type of inverse z -transform (left-sided, right-sided, or two-sided sequences) ass

8、ociated with each of these ROCs .(3) (3) Give the expression of right-sided sequence.3. A real 8-point sequence .Its 8-point DFT is Xk.(1) Determine the values of ,.(2) (2) Supposing.Sketch . (3) (3) Determine the value of .4. Let =1 2 1 1,and =1 1 1,. (1) (1) Sketch the linear convolution .(2) (2)

9、denote the N-point circular convolution .Determine the values of ,. Explain which value is equal to the value of.Digital Signal Processing3 Note: Give the answer of the following problems as possible in English.1.（20 points）A length-8 sequence is given by . Please give its expressions of ZT , DTFTan

10、d 8-point DFT in closed-form.2.（20 points）Consider a length-8 real sequence, defined for , with 8-point DFT ,.(1) Calculate the following values of without computing the DFT itself: (a) , (b) , (c) .(2) Sketch the sequence whose 8-point DFT is given by .3. (18points) A causal LTI discrete-time syste

11、m has the difference equation .(4) (1) Determine the transfer function of the system.(5) (2) Give the pole-zero plot of the system.(6) (3) Determine the impulse response of the system.4. (15 points) The frequency response of a linear phase FIR filter is given by .(1) (1) Determine and sketch the imp

12、ulse response of the filter.(2) (2) Which type is this linear phase FIR filter?5. (15 points) Using bilinear method , design a digital 2nd-order Butterworth lowpass filter which has the cut-off frequency .(1) (1) Give the transfer function of the designed filter.(2) (2) Develop a realization structu

13、re of the designed filter in cannonic form.Note: The transfer function of analog 2nd-order Butterworth lowpass filter with 3-dB cut-off frequency is .6. (12 points) Let be an order-63 FIR filter, and be a length-64 sequence. The input-output relationship of the filter is shown as following figure. P

14、lease write a MATLAB program to compute by FFT , plot the magnitude and phase spectrum of .5. 5. A sequencehas DTFT shown as following figure. Sketch DTFTof . If and ,where and .Give the expression between and .Test Of Digital Signal Processing4（Give the answer of the following problems in English a

15、s possible as you can）1 1 A sequenceis known as below: , where (1) Sketch the real part of .(2) If A=1, is it periodic? If it is, give its period.2 2 For each of the following discrete-time systems, where yn and xn are, respectively, the output and the input sequences, determine whether or not the s

16、ystem is (1)linear, (2)causal ,(3) stable,(4)shift-invariant.Where .3 3 Calculate the corresponding transformation of following functions:(1) Known , its 1024-point DFT is wanted.(2) Known , its DTFT is wanted.(3) Known , its IDTFT is wanted.4 4 Xk, 0 k 7, is the 8-point DFT of sequence xn= -1, 2, -

17、3, 2, 0, -4, 6, 2, 0 k 7. Please calculate the following values without computing DFT:(a) ; (b) ; (c) ; (d) .5 5 Given two sequences: gn=1 2 3 4(), hn=5 0 3 ().(1) Determine the linear convolution of the two sequence *.(2) Determine the circular convolution of the two sequence Nfor N=4 and N=6, Whil

18、e the lengths of sequences less than N, do the zero-padding. (3) From the results of (1) and (2), make the conclusion of how to use circular convolution to help calculating linear convolution.6. Consider the z - transform as below: .(7) (1) Give the pole-zero plot of .(8) (2) Determine all possible

19、ROCs of . Discuss the type of inverse z -transform (left-sided, right-sided, or two-sided sequences) associated with each of these ROCs .(9) (3) Can you find the? If it is possible, what is it?Test Of Digital Signal Processing（Give the answer of the following problems in English as possible as you c

20、an）6 1 A sequenceis known as below: , where (1) Sketch the real part of .(2) If A=1, is it periodic? If it is, give its period.7 2 For each of the following discrete-time systems, where yn and xn are, respectively, the output and the input sequences, determine whether or not the system is (1)linear,

21、 (2)causal ,(3) stable,(4)shift-invariant.Where .8 3 Calculate the corresponding transformation of following functions:(1) Known , its 1024-point DFT is wanted.(2) Known , its DTFT is wanted.(3) Known , its IDTFT is wanted.9 4 Xk, 0 k 7, is the 8-point DFT of sequence xn= -1, 2, -3, 2, 0, -4, 6, 2, 0 k 7. Please calculate the following values without computing DFT:(a) ;