數(shù)字信號處理實驗二(共16頁)

1、Student Number:20111060021Laboratory Exercise 2DISCRETE-TIME SYSTEMS: TIME-DOMAIN REPRESENTATION2.1SIMULATION OF DISCRETE-TIME SYSTEMSProject 2.1The Moving Average System A copy of Program P2_1 is given below:%程序(chngx)P2.1%一個M點滑動(hudng)平均濾波器的仿真%產(chǎn)生(chnshng)輸入信號clf;n=0:100;s1=cos(2*pi*0.05*n);%一個低頻正弦

2、s2=cos(2*pi*0.47*n);%一個高頻正弦x=s1+s2;%滑動平均濾波器的實現(xiàn)M=input(濾波器所需的長度= );num=ones(1,M);y=filter(num,1,x)/M;%顯示輸入和輸出信號subplot(2,2,1);plot(n,s1);axis(0,100,-2,2);xlabel(時間序號 n);ylabel(振幅);title(信號#1);subplot(2,2,2);plot(n,s2);axis(0,100,-2,2);xlabel(時間序號 n);ylabel(振幅);title(信號#2);subplot(2,2,3);plot(n,x);axi

3、s(0,100,-2,2);xlabel(時間序號 n);ylabel(振幅);title(輸入(shr)信號);subplot(2,2,4);plot(n,y);axis(0,100,-2,2);xlabel(時間(shjin)序號 n);ylabel(振幅(zhnf);title(輸出信號);axis;Answers:Q2.1 The output sequence generated by running the above program for M = 2 with xn = s1n+s2n as the input is shown below. The component of

4、the input xn suppressed by the discrete-time system simulated by this program is -Signal#2,thehighfrequencyone(itisalowpassfilter). Q2.2 Program P2_1 is modified to simulate the LTI system yn = 0.5(xnxn1) and process the input xn = s1n+s2n resulting in the output sequence shown below:n=0:100;s1=cos(

5、2*pi*0.05*n);s2=cos(2*pi*0.47*n);x=s1+s2;M=input(濾波器所需的長度(chngd)= );num=(-1).0:M-1;y=filter(num,1,x)/M;clf;subplot(2,2,1);plot(n,s1);axis(0,100,-2,2);xlabel(時間(shjin)序號 n);ylabel(振幅(zhnf);title(信號#1);subplot(2,2,2);plot(n,s2);axis(0,100,-2,2);xlabel(時間序號 n);ylabel(振幅);title(信號#2);subplot(2,2,3);plot

6、(n,x);axis(0,100,-2,2);xlabel(時間序號 n);ylabel(振幅);title(輸入信號);subplot(2,2,4);plot(n,y);xlabel(時間序號 n);ylabel(振幅);title(輸出信號);axis;The effect of changing the LTI system on the input is -Thesystemisnowahighpassfilter.Itpassesthehighfrequencyinputcomponents2insteadofthelowfrequencyinputcomponents1.Q2.4

7、The required modifications to Program P2_1 by changing the input sequence to a swept-frequency sinusoidal signal (length 101, minimum frequency 0, and a maximum frequency 0.5) as the input signal (see Program P1_7) are listed below:n=0:100;a=pi/200;b=0;arg=a*n.*n+b*n;x=cos(arg);M=input(濾波器所需的長度(chng

8、d)= );num=ones(1,M);y=filter(num,1,x)/M;clf;subplot(2,1,1);plot(n,x);axis(0,100,-1.5,1.5);xlabel(時間(shjin)序號 n);ylabel(振幅(zhnf);title(輸入信號);subplot(2,1,2);plot(n,y);axis(0,100,-1.5,1.5);xlabel(時間(shjin)序號 n);ylabel(振幅(zhnf);title(輸出(shch)信號);axis;The output signal generated by running this program i

9、s plotted below. The results of Questions Q2.1 and Q2.2 from the response of this system to the swept-frequency signal can be explained as follows:weseeagainthatthissystemisalowpassfilter.Attheleftofthegraphs,theinputsignalisalowfrequencysinusoidthatispassedtotheoutputwithoutattenuation.Asnincreases

10、,thefrequencyoftheinputrises,andincreasingattenuationisseenattheoutput.InQ2.1,theinputwasasumoftwosinusoidss1ands2withf1=0.05andf2=0.47.ThesweptfrequencyinputofQ2.4reachesafrequencyof0.05atn=10,wherethereisvirtuallynoattenuationintheoutputshownabove.This“explains”whys1waspassedbythesysteminQ2.1.Thes

11、weptfrequencyinputofQ2.4reachesafrequencyof0.47atapproximatelyn=94,wheretheattenuationofthesystemissubstantial.This“explains”whys2wasalmostcompletelysuppressedintheoutputinQ2.1.ThereisnodirectrelationshipbetweentheresultshownaboveforQ2.4andtheresultobtainedinQ2.2.However,usingfrequencydomainconcepts

12、(Chapter3)wecanreasonthat,ifthesweptfrequencysignalwasinputtothesystemyn=0.5(xnxn-1),wewouldseearesultoppositetowhatisshownabove.Sincethesystemwouldthenbeahighpassfilter,therewouldbesubstantialattenuationoftheoutputattheleftsideofthegraphandvirtuallynoattenuationattherightsideofthegraph.This“explain

13、s”whyinQ2.2thelowfrequencycomponents1wassuppressedinthesystemoutput,whereasthehighfrequencycomponents2waspassed.Project 2.3Linear and Nonlinear SystemsA copy of Program P2_3 is given below:%程序(chngx)P2.3%生成(shn chn)輸入序列clf;n=0:40;a=2;b=-3;x1=cos(2*pi*0.1*n);x2=cos(2*pi*0.4*n);x=a*x1+b*x2;num=2.2403

14、2.4908 2.2403;den=1 -0.4 0.75;ic=0 0;%設(shè)置(shzh)零初始條件y1=filter(num,den,x1,ic);%計算輸出y1ny2=filter(num,den,x2,ic);%計算輸出y2ny=filter(num,den,x,ic);%計算輸出ynyt=a*y1+b*y2;d=y-yt;%計算差值輸出dn%畫出輸出和差信號subplot(3,1,1)stem(n,y);ylabel(振幅);title(加權(quán)輸入:acdot x_1n+bcdot x_2n的輸出);subplot(3,1,2)stem(n,yt);ylabel(振幅);title(加

15、權(quán)輸入:acdot y_1n+bcdot y_2n的輸出);subplot(3,1,3)stem(n,d)xlabel(時間序號n);ylabel(振幅);title(差信號(xnho);Answers:Q2.7The outputs yn, obtained with weighted input, and ytn, obtained by combining the two outputs y1n and y2n with the same weights, are shown below along with the difference between the two signals:

16、The two sequences are - The same up to numerical roundoff. The system is - Linear.Project 2.4Time-invariant and Time-varying SystemsA copy of Program P2_4 is given below:%程序(chngx)P2.4%生成(shn chn)輸入序列clf;n=0:40;D=10;a=3;b=-2;x=a*cos(2*pi*0.1*n)+b*cos(2*pi*0.4*n);xd=zeros(1,D) x;num=2.2403 2.4908 2.2

17、403;den=1 -0.4 0.75;ic=0 0;%設(shè)置(shzh)零初始條件%計算(j sun)輸出yny=filter(num,den,x,ic);%計算(j sun)輸出ydnyd=filter(num,den,xd,ic);%計算差值輸出dnd=y-yd(1+D:41+D);%畫出輸出subplot(3,1,1)stem(n,y);ylabel(振幅);title(輸出yn);grid;subplot(3,1,2)stem(n,yd(1:41);ylabel(振幅);title(延時輸出);grid;subplot(3,1,3)stem(n,d);xlabel(時間序號 n);yl

18、abel(振幅);title(差值信號);grid;Answers:Q2.12 The output sequences yn and ydn-10 generated by running Program P2_4 are shown below - These two sequences are related as follows - yn-10=ydnThe system is - Time Invariant2.2LINEAR TIME-INVARIANT DISCRETE-TIME SYSTEMSProject 2.5Computation of Impulse Responses

19、 of LTI SystemsA copy of Program P2_5 is shown below:%程序(chngx)P2.5%計算(j sun)沖激響應(yīng)yclf;N=40;num=2.2403 2.4908 2.2403;den=1 -0.4 0.75;y=impz(num,den,N);%畫出沖激響應(yīng)stem(y);xlabel(時間(shjin)序號n);ylabel(振幅);title(沖激響應(yīng));grid;Answers:Q2.19 The first 41 samples of the impulse response of the discrete-time system

20、 of Project 2.3 generated by running Program P2_5 is given below:Q2.20 The required modifications to Program P2_5 to generate the impulse response of the following causal LTI system:yn + 0.71yn-1 0.46yn-2 0.62yn-3= 0.9xn 0.45xn-1 + 0.35xn-2 + 0.002xn-3are given below:clf;N=45;num=0.9 -0.45 0.35 0.00

21、2;den=1.0 0.71 -0.46 -0.62;y=impz(num,den,N);stem(y);xlabel(時間(shjin)序號n);ylabel(振幅(zhnf);title(沖激響應(yīng));grid;The first 45 samples of the impulse response of this discrete-time system generated by running the modified is given below:Project 2.6Cascade of LTI SystemsA copy of Program P2_6 is given below

22、:%程序(chngx)P2.6%級聯(lián)實現(xiàn)(shxin)clf;x=1 zeros(1,40);%生成(shn chn)輸入n=0:40;%四階系統(tǒng)的系數(shù)den=1 1.6 2.28 1.325 0.68;num=0.06 -0.19 0.27 -0.26 0.12;%計算四階系統(tǒng)的輸出y=filter(num,den,x);%兩個二階系統(tǒng)的系數(shù)num1=0.3 -0.2 0.4;den1=1 0.9 0.8;num2=0.2 -0.5 0.3;den2=1 0.7 0.85;%級聯(lián)第一級的輸出(shch)y1ny1=filter(num1,den1,x);%級聯(lián)第二級的輸出(shch)y2ny

23、2=filter(num2,den2,y1);%y和y2n之間的差d=y-y2;%畫出輸出(shch)和差值信號subplot(3,1,1);stem(n,y);ylabel(振幅);title(四階實現(xiàn)的輸出);grid;subplot(3,1,2);stem(n,y2);ylabel(振幅);title(級聯(lián)實現(xiàn)的輸出);grid;subplot(3,1,3);stem(n,d);xlabel(時間序號 n);ylabel(振幅);title(差值信號);grid; Q2.23 The output sequences yn, y2n, and the difference signal

24、dn generated by running Program P2_6 are indicated below: The relation between yn and y2n is - They are the same up to numerical roundoffProject 2.7ConvolutionA copy of Program P2_7 is reproduced below:%程序(chngx)P2.7clf;h=3 2 1 -2 1 0 -4 0 3;%沖激(chn j)x=1 -2 3 -4 3 2 1;%輸入(shr)序列y=conv(h,x);n=0:14;s

25、ubplot(2,1,1);stem(n,y);xlabel(時間序號n);ylabel(振幅);title(用卷積得到的輸出);grid;x1=x zeros(1,8);y1=filter(h,1,x1);subplot(2,1,2);stem(n,y1);xlabel(時間序號n);ylabel(振幅(zhnf);title(用濾波器生成(shn chn)的輸出);grid;Answers:Q2.28 The sequences yn and y1n generated by running Program P2_7 are shown below:The difference betwe

26、en yn and y1n is - They are the same.The reason for using x1n as the input, obtained by zero-padding xn, for generating y1n is - FortwosequencesoflengthN1andN2,convreturnstheresultingsequenceoflengthN1+N2-1.Bycontrast,filteracceptsaninputsignalandasystemspecification.Thereturnedresultisthesamelengthastheinputsignal.Therefore,toobtaindirectlycomparableresultsfromconvandfilt,itisnecessarytosupplyfiltwithaninputthathasbeenzeropaddedouttolengthlength(x)+length(h)-1.Project 2.8Stability of LTI SystemsA copy of Program