东南大学Matlab作业2.doc

Matlab Worksheet 2Part A (In-class room exercises)1. Using plot to display the following voltage with appropriate line type, title and labels. Also present the graph with suitable ranges of axis.where f=50 Hz.(Hint: time interval must be small enough, e.g. 0.001 seconds. Therefore, t=0:0.001:1 is appropriate);Answer:Home_work_2_A_1.m%lbs in-class-exercise1_1 2013/8/21%function Using plot to display the following voltage with appropriate line type, title and labels. Also present the graph with suitable ranges of axis. % v(t)=220sin(2?ft)% where f=50 Hz.%Comment/loop clear all; close all;t=0:0.001:1;v=220*sin(2*pi*50*t);plot(t,v,m,LineWidth,2)xlabel(t(sec)ylabel(v(voltage)title(v(t)=220sin(2?ft)axis(0 0.2 -260 260);grid on; 2. Using plot to display the following voltage with appropriate line type, title and labels. Also present the graph with suitable ranges of axis.where f=50 Hz.In addition, on the same graph, draw the envelope of the oscillation and add legends. Answer:home_work_2_A_2.m%lbs in-class-exercise1_2 2013/8/21%function Using plot to display the following voltage with appropriate line type, title and labels. Also present the graph with suitable ranges of axis.% v(t)=220exp(-5t)cos(2?ft)% where f=50 Hz.% In addition, on the same graph, draw the envelope of the oscillation and add legends. %Comment/loop clear all; close all;t=0:0.001:1;v=220*exp(-5*t).*sin(2*pi*50*t); plot(t,v,m,LineWidth,2);xlabel(t(sec)ylabel(v(voltage)title(v(t)=220exp(-5t)cos(2?ft)hold on;v1=220*exp(-5*t);plot(t,v1,b,LineWidth,2);hold on;plot(t,-v1,b,LineWidth,2);hold off;legend(the oscillation, the envelope of the oscillation);axis(0 1 -220 220);grid on; 3. Use subplot, draw a 2 by 2 array of plots for the following functions:Apply appropriate line type, title, labels and axis ranges for the graphs.Answer:home_work_2_A_3.m%lbs in-class-exercise1_3 2013/8/21%function Use subplot, draw a 2 by 2 array of plots for the following functions:% v1=cos(10*pi*t);v2=exp(-5*t).*v1;v3=exp(-10*t).*v1;v4=exp(-20*t).*cos(10*pi*t)% Apply appropriate line type, title, labels and axis ranges for the graphs.%Comment/loop t=0:0.001:1; v1=cos(10*pi*t); v2=exp(-5*t).*v1; v3=exp(-10*t).*v1; v4=exp(-20*t).*cos(10*pi*t);subplot(2,2,1)plot(t,v1,k,LineWidth,2)xlabel(t(sec)ylabel(v(voltage)title(v(t)=cos(10?t);axis(0 1 -1 1) subplot(2,2,2)plot(t,v2,r,LineWidth,2)xlabel(t(sec)ylabel(v(voltage)title(v(t)=exp(-5t)cos(10?t);axis(0 1 -1 1) subplot(2,2,3)plot(t,v3,g,LineWidth,2)xlabel(t(sec)ylabel(v(voltage)title(v(t)=exp(-10t)cos(10?t);axis(0 1 -1 1) subplot(2,2,4)plot(t,v4,m,LineWidth,2)xlabel(t(sec)ylabel(v(voltage)title(v(t)=exp(-20t)cos(10?t);axis(0 1 -1 1) 4. Use plot3 to plot 2 spiral curves like below with appropriate line width and colour.Answer:(1) home_work_2_A_4_1.mt=0:0.01:10;x=sin(2*pi*t).*exp(0.35*t-1);y=cos(2*pi*t).*exp(0.35*t-1);z=0.25*t;plot3(x,y,z,g,LineWidth,2);axis(-15 15 -15 15 0 3);grid on;(2)home_work_2_A_4_2.mt=0:0.01:10;x=1.5*t.*sin(2*pi*t);y=1.5*t.*cos(2*pi*t);z=0.2*t;plot3(x,y,z,r,LineWidth,3);axis(-15 15 -15 15 0 2);grid on;5. Display the surface using mesh and contour with a suitable resolution:Answer:home_work_2_A_5.mx,y = meshgrid(0:1:100, 0:1:100);z=exp(-0.005.*(x-50).2+(y-50).2);figure(1);mesh(x,y,z),xlabel(x), ylabel(y), grid on;figure(2);contour(x,y,z),xlabel(x), ylabel(y), grid on; 6. Load 2 of your photos into Matlab WorkSpace using imread. a) Change brightness locally or globally. b) Overlap them to produce a new photo. c) write a new photo into a file using imwrite. (Note: lower version of Matlab such as 6.5 is not allowed to do some direct image operations.) Answer:a) home_work_2_A_6_a.mclear all;close all;A=imread(lbs.jpg);figure(1); subplot(2, 2, 1);imshow(A),title(初始图像);size(A); subplot(2,2,2);B=histeq(A(:,:,1); % Enhance contrast using histogram equalization.imshow(B),title(对比度增大处理); subplot(2,2,3);C=imadjust(A,0.3,0.7,);imshow(C),title(亮度调节处理); subplot(2,2,4);D=imfilter(A,2);imshow(D),title(真彩色增强处理);b） home_work_2_A_6_b.mA=imread(lbs.jpg);B=imread(man.jpg);M,N,L=size(A);C(1:M,1:N,1:L)=B(1:M,1:N,1:L);figure(1);imshow(A);title(figure1);figure(2);imshow(C);title(figure2);figure(3);imshow(A+C);title(figure3);c) home_work_2_A_6_c.mA=imread(lbs.jpg);B=imadjust(A,0.2,0.6,);imwrite(B,lbs1.jpg);imshow(lbs1.jpg);7. For linear simultaneous equationsthe equation coefficients:A= 1 -1 4 3 -5 4 5 -6 0 7 -8 9 -1 3 -2 6; (M=N)a) Find the determinant of A,b) Find the inverse of A and check for matrix singularity,c) If B= 5; 1; -2; 3, find the unknown x in the equation. Answer:home_work_2_A_7.m A= 1 -1 4 3; -5 4 5 -6; 0 7 -8 9; -1 3 -2 6;disp(a) determinant of A);det(A)disp(b) the inverse of A and check for matrix singularity);inv(A)cond(A)B= 5; 1; -2; 3disp(c) the solution of the equation);x=inv(A)*Bresult: home_work_2_A_7a) determinant of Aans = -765.0000b) the inverse of Aand check for matrix singularityans = 0.3333 -0.0000 0.3333 -0.6667 0.2000 0.1176 0.2706 -0.3882 0.2000 0.0588 0.0353 -0.0941 0.0222 -0.0392 -0.0680 0.2183ans = 16.4186B = 5 1 -2 3c) the solution of the equationx = -1.0000 -0.5882 0.7059 0.86278. For linear simultaneous equations,MN, the equation coefficients:A= 1 -1 4 3 -5 4 5 -6 0 7 -8 9 -1 3 -2 6 1 -2 5 30 4 7 -3; a) Find the determinant of A*A,b) Find the inverse of A*A and check for matrix singularity,c) If B= 5; 1; -2; 3; 4; 0, find the solution of the equation.Answer:home_work_2_A_8.m A= 1 -1 4 3; -5 4 5 -6; 0 7 -8 9; -1 3 -2 6; 1 -2 5 3; 0 4 7 -3; disp(a) determinant of A*A);det(A*A)disp(b) the inverse of A*A and check for matrix singularity);inv(A*A)cond(A*A)B= 5; 1; -2; 3; 4; 0;disp(c) the solution of the equation);x=inv(A*A)*A*Bresult: home_work_2_A_8a) determinant of A*Aans = 2.1051e+07b) the inverse of A*A and check for matrix singularityans = 0.0884 0.0321 -0.0013 -0.0219 0.0321 0.0231 0.0002 -0.0099 -0.0013 0.0002 0.0085 0.0053 -0.0219 -0.0099 0.0053 0.0144ans = 32.5278c) the solution of the equationx = -0.8903 -0.4898 0.5755 0.70839. Data of 10 records are shown belowy=3.5 4.3 3.7 5.4 6.6 7.3 8.7 8.8 9.4 9.0 10.0 12.0 11.3 9.9 13.3,Use polyfit with different orders (from 1 to 3) of polynomials to find a curve of best fit. Check the total distance between the fitted curve z and records defined by.Answer:home_work_2_A_9.mclear all;close all;x=1:1:15;y=3.5 4.3 3.7 5.4 6.6 7.3 8.7 8.8 9.4 9.0 10.0 12.0 11.3 9.9 13.3;plot(x,y,ro); hold on; p=polyfit(x,y,1);z=polyval(p,x);plot(x,z,bx);hold on;disp(一阶拟合误差);s1=sqrt(sum(z-y).2) p=polyfit(x,y,2);z=polyval(p,x);plot(x,z,kx,Linewidth,1.5);hold on;disp(二阶拟合误差);s2=sqrt(sum(z-y).2) p=polyfit(x,y,3);z=polyval(p,x);plot(x,z,r-,linewidth,2);hold off;grid on;legend(point,polyfit 1,polyfit 2,polyfit 3);disp(三阶拟合误差);s3=sqrt(sum(z-y).2)result： home_work_2_A_9一阶拟合误差s1 = 3.2807二阶拟合误差s2 = 3.0399三阶拟合误差s3 = 3.039810. Create a set of 20 points from a curve by Matlab code:x=1:20;y=2*exp(-0.3*(x-5).2)+0.7*exp(-0.2*(x-12).2);Then interpolate the curve to 60 points using linear and spline options, respectively. See the quality of different types of interpolation.Answer:home_work_2_A_10.mclear all,close all;x=1:20;y=2*exp(-0.3*(x-5).2)+0.7*exp(-0.2*(x-12).2);plot(x,y,ro,LineWidth,2);hold on;xi=1:1/3:20;yi = interp1(x,y,xi,linear);plot(xi,yi,b*);hold on;yi = interp1(x,y,xi,spline);plot(xi,yi,m-);legend(point,linear,spline)hold off;Part B1. Using the plot and subplot functions create 4 plots on a 2 by 2 array of subplots, for the function exp(-t)sin(5t) showing in each plot the function in the corresponding intervals of t i.e. (-2, -1), (-1,0), (0,1) and (1,2). Answer:home_work_2_B_1.mt=-2:0.01:-1;v=exp(-t).*sin(5*t);subplot(2,2,1);plot(t,v,m,LineWidth,2); t=-1:0.01:0;subplot(2,2,2);plot(t,v,b,LineWidth,2); t=0:0.01:1;subplot(2,2,3);plot(t,v,r,LineWidth,2); t=1:0.01:2;subplot(2,2,4);plot(t,v,k,LineWidth,2);2. A three phase induction motor characteristic is given in terms of mechanical shaft output torque (NM Newton-meter) as a function of rotational speed (rad/s radian per second). This is approximated by 3 piece-wise linear equations as follows:This motor is directly coupled to a load , which can be represented as Write 2 separate Matlab function m-files in which: a) the motor characteristic, b) the load characteristic are defined only as functions of . Name them motor.m and sysload.m, respectively.Answer:a) motor.mfunction Tm = motor( w )for i=1:length(w);if w(i)=0 & w(i)=90*pi & w(i)=110*pi & w(i) motor(0)ans = 4 w=0:12*pi; motor(w)ans = Columns 1 through 10 4.0000 4.0035 4.0071 4.0106 4.0141 4.0177 4.0212 4.0248 4.0283 4.0318 Columns 11 through 20 4.0354 4.0389 4.0424 4.0460 4.0495 4.0531 4.0566 4.0601 4.0637 4.0672 Columns 21 through 30 4.0707 4.0743 4.0778 4.0813 4.0849 4.0884 4.0920 4.0955 4.0990 4.1026 Columns 31 through 38 4.1061 4.1096 4.1132 4.1167 4.1203 4.1238 4.1273 4.1309b) sysload.mfunction Tl = sysload( w )Tl=-50*(w/(120*pi).3+100*(w/(120*pi).2+4*w./(120*pi);endresult: sysload(0)ans = 0 w=0:12*pi; sysload(w)ans = Columns 1 through 10 0 0.0113 0.0240 0.0381 0.0536 0.0705 0.0888 0.1084 0.1294 0.1518 Columns 11 through 20 0.1755 0.2006 0.2270 0.2548 0.2839 0.3143 0.3461 0.3791 0.4135 0.4492 Columns 21 through 30 0.4862 0.5245 0.5640 0.6049 0.6470 0.6904 0.7351 0.7810 0.8282 0.8767 Columns 31 through 38 0.9264 0.9773 1.0295 1.0828 1.1375 1.1933 1.2503 1.30863. Write a Matlab scripgt-m file which calls your function m-files from Question 2. And plot the motor and load characterstics on the same figure, giving suitable labelling and title. Name this script m-file systemplot.mAnswer:home _work_2_B_3.mw=0:pi/20:120*pi;Tm=motor(w);plot(w,Tm,m,LineWidth,2);hold on;Tl=sysload(w);plot(w,Tl,r,LineWidth,2);hold off;xlabel(speed w(rad/s_);ylabel(torque(NM Newton-meter);title(the motor and load characterstics);legend(motor line,sysload line)4. Write a sript m-file which finds all the mathematicall possible points (values of ) where5. for the range 0 120 (rad/s) with the characteristic given in Question 2. The system could theoretically operate at a speed where Mathematically, this involves finding the roots of the equationGive a name to this m-file posspoints.m . Call posspoints.m in systemplot.m and show all of the points on a system plot using the o symbol.Answer:(1)subfun.mfunction sub = subfun( w )for i=1:length(w);if w(i)=0 & w(i)=90*pi & w(i)=110*pi & w(i) posspoints xx = 74.0177 307.6718 360.7836(3)systemplot.mw=0:pi/20:120*pi;Tm=motor(w);plot(w,Tm,m,LineWidth,2);hold on;Tl=sysload(w);plot(w,Tl,r,LineWidth,2);hold on;xlabel(speed w(rad/s_);ylabel(torque(NM Newton-meter);title(the motor and load characterstics);legend(motor line,sysload line)posspoints;Tl=-50*(x/(120*pi).3+100*(x/(120*pi).2+4*x/(120*pi)plot(x,Tl,ko,LineWidth,2);hold off;grid on; posspoints xx = 74.0177 307.6718 360.7836Part CIntroduction to DSP1. Basic digital signalsUnit impulse functionExercise 1-1: Display the unit impulse function with Matlab code. The code can be either typed under Matlab prompt or written into a script Matlab file, then run the file.n=-10:10;for k=1:21 x(k)=0;end;x(11)=1;stem(n, x);axis(-10 10 0 2);Problem 1-1: For the signal, write the Matlab code and copy the result figure into the following boxes.n=-10:10;for k=1:21 x(k)=0;end;x(9)=2;stem(n, x);axis(-10 10 0 2); Unit step functionExercise 1-2: Display the unit step function with Matlab code: n=-10:10;for k=1:10 x(k)=0;end; for k=11:21 x(k)=1;end;stem(n, x);axis(-10 10 0 2);Problem 1-2: For the signal , write the Matlab code, and display the corresponding signal into the following boxes.n=-10:10;for k=1:12 x(k)=0;end; for k=13:21 x(k)=-1;end;stem(n, x); axis(-10 10 -2 1); Sine wave where w - frequency (rad/second), T - sampling interval (seconds)Exercise 1-3: Let T=0.02, w =6.28. Using the following code, plot on the screen in the region 0 n 100.n=0:100;T=0.02;omega=6.28;for k=1:101 x(k)=sin(k-1)*omega*T);end;stem(n, x);Problem 1-3: Modify the above code to display the signal: , where T=0.02, w=6.28. Execute the code and plot the signal on the screen. Copy the code, then display the signal into the following boxes.n=0:100;T=0.02;omega=6.28; for k=1:101 x(k)=2*sin(k-1)*omega*T+pi/2);end;stem(n, x);Time shift, impulse and step responses Exercise 1-4For the unit impulse, and the unit stepwrite two Matlab functions and save as impseq.m and stepseq.m files, respectively.% impseq.m %Unit Impulse %n1:n2 simple number range%n0 - time shiftfunction x, n=impseq(n0,n1,n2)n=n1:n2;x=(n-n0)=0;%end;% stepseq.m % Unit Step%n1:n2 simple number range%n0 - time shiftfunction x, n= stepseq(n0, n1, n2)n=n1:n2;x=(n-n0)=0;%endGiven the following difference equation:a) Calculate and plot the impulse response at n=-20,120; andb) Calculate and plot the step response at n=-20,120, using the following codeb=1; a=1,-0.7, 0.9;x=impseq(0,-20, 120); n=-20:120;h=filter(b,a,x);subplot(2,1,1);stem(n,h);title(Impulse response);xlabel(n);ylabel(h(n); x=stepseq(0,-20, 120); n=-20:120;h=filter(b,a,x);subplot(2,1,2);stem(n,h);title(Step response);xlabel(n);ylabel(s(n);Problem 1-4 Solve the above a) and b) for the system:Display the responses in the boxes.b=1,2; a=1,-1.8 , 0.94;x=impseq(0,-20, 120); n=-20:120;h=filter(b,a,x);subplot(2,1,1);stem(n,h);title(Impulse response);xlabel(n);ylabel(h(n); x=stepseq(0,-20, 120); n=-20:120;h=filter(b,a,x);subplot(2,1,2);stem(n,h);title(Step response);xlabel(n);ylabel(s(n);2. ConvolutionIn the liner time-invariant (LTI) system, the response of the system can be calculated by a convolution between the input and its unit impulse response.Exercise 2-1 Write an Matlab function and save as conv_m.m. %convolution function %conv_m.mfunction y, ny=conv_m(x,nx,h,nh)nyb=nx(1)+nh(1);nye=nx(length(x)+nh(length(h);ny=nyb:nye;y=conv(x,h);%end;Compute the convolution for xn and hn using the following codes:x=3, 11, 7, 0, -1, 4, 2;nx=-3:3;h=2, 3, 0, -5, 2, 1;nh=-1:4;y, ny=conv_m(x,nx,h,nh);Subplot(3,1,1);stem(nx,x);ylabel(xn);axis(-6 10 -20 20);Subplot(3,1,2); stem(nh,h);ylabel(hn);axis(-6 10 -20 20);subplot(3,1,3);stem(ny,y);xlabel(n);ylabel(yn);axis(-6 1