MATLAB Examples

## Contents

set(0,'defaultFigureColor',[1 1 1]); clear all; clc; % Use the following external package at Matlab Central: 
addpath([pwd '\ds2nfu']); isVideOn = 0; % To control whether to dump jpeg snapshots or not. 0: do not dump 1: dump jpegs Np = 220; % Number of spatial points dx = 2*pi/Np; % discretization size x = 0:dx:(6*pi); % utilized x range % Individual Harmonics A=4; f1sin = A*sin(x)/pi; f1cos = A*cos(x)/pi; f2sin = A*sin(3*x)/(3*pi); f2cos = A*cos(3*x)/(3*pi); f3sin = A*sin(5*x)/(5*pi); f3cos = A*cos(5*x)/(5*pi); f4sin = A*sin(7*x)/(7*pi); f4cos = A*cos(7*x)/(7*pi); f5sin = A*sin(9*x)/(9*pi); f5cos = A*cos(9*x)/(9*pi); 

Overall signal (square wave to be synthesized)

f=f1sin+f2sin+f3sin+f4sin+f5sin; Nt = 100; % Number of points over the circles dtheta = 2*pi/Nt; % Discretization over circles theta = 0:dtheta:2*pi; % Span the whole 2pi % Circle points x1=A/pi*cos(theta); y1=A/pi*sin(theta); x2=A/(3*pi)*cos(3*theta); y2=A/(3*pi)*sin(3*theta); x3=A/(5*pi)*cos(5*theta); y3=A/(5*pi)*sin(5*theta); x4=A/(7*pi)*cos(7*theta); y4=A/(7*pi)*sin(7*theta); Lx=length(x); Lw=2; Fs=12; 

## First Part: Just shows individual circles and corresponding sinusoids

for i=1:length(x) %disp([num2str(i) ' of ' num2str(Lx)]) f1=figure (2); clf; sp1=subplot(1,2,1); % -- 1st harmonic --- plot(x1,y1,'LineWidth',Lw,'Color','b'); hold on; grid on; line([0 f1cos(i)],[0 f1sin(i)],'Color','b','LineWidth',Lw,'LineSmoothing','on'); set(sp1,'Position',[0.0400 0.1800 0.4 0.677]); xlim([-2.5 2.5]); ylim([-2.5 2.5]) [xf1, yf1] = ds2nfu(sp1,f1cos(i),f1sin(i)); % Convert axes coordinates to figure coordinates for 1st axes line(f1cos(i),f1sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','b','color','b') % -- 2nd harmonic --- plot(x2,y2,'LineWidth',Lw,'Color','r'); hold on; line([0 f2cos(i)],[0 f2sin(i)],'Color','r','LineWidth',Lw,'LineSmoothing','on'); line(f2cos(i),f2sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','r','color','r') [xf2, yf2] = ds2nfu(f2cos(i),f2sin(i)); % Convert axes coordinates to figure coordinates for 1st axes % -- 3rd harmonic --- plot(x3,y3,'LineWidth',Lw,'Color','g'); hold on; line([0 f3cos(i)],[0 f3sin(i)],'Color','g','LineWidth',Lw,'LineSmoothing','on'); line(f3cos(i),f3sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','g','color','g') [xf3, yf3] = ds2nfu(f3cos(i),f3sin(i)); % Convert axes coordinates to figure coordinates for 1st axes title('Harmonic Circles','FontSize',Fs,'FontName','Century Gothic') set(gca,'FontSize',Fs,'FontName','Century Gothic'); %'Aharoni'); sp2=subplot(1,2,2); % -- 1st harmonic --- plot(x(1:i),f1sin(1:i),'LineWidth',Lw,'Color','b'); hold on; grid on; ylim([-2.5 2.5]); xlim([0 19]) set(sp2,'Position',[0.48 0.178200 0.49 0.680]); % Convert axes coordinates to figure coordinates for 1st axes [xg1, yg1] = ds2nfu(x(i),f1sin(i)); annotation('line',[xf1 xg1],[yf1 yg1],'color','b','LineStyle','--','LineWidth',Lw); % -- 2nd harmonic --- plot(sp2,x(1:i),f2sin(1:i),'g','LineWidth',Lw,'Color','r'); hold on; grid on; [xg2, yg2] = ds2nfu(x(i),f2sin(i)); % Convert axes coordinates to figure coordinates for 1st axes annotation('line',[xf2 xg2],[yf2 yg2],'color','r','LineStyle','--','LineWidth',Lw); % -- 3rd harmonic --- plot(x(1:i),f3sin(1:i),'k','LineWidth',Lw,'Color','g'); hold on; grid on; [xg3, yg3] = ds2nfu(x(i),f3sin(i)); % Convert axes coordinates to figure coordinates for 1st axes annotation('line',[xf3 xg3],[yf3 yg3],'color','g','LineStyle','--','LineWidth',Lw); line(x(i),f1sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','b','color','b') line(x(i),f2sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','r','color','r') line(x(i),f3sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','g','color','g') title('Harmonics','FontSize',Fs,'FontName','Century Gothic') legend('4sin(x)/\pi','4sin(3x)/3\pi','4sin(5x)/5\pi'); xlabel('x','FontSize',Fs,'FontName','Century Gothic') set(gca,'FontSize',Fs,'FontName','Century Gothic'); %'Aharoni'); % --------------------------------------------------------------------- if (isVideOn == 1) set(gcf,'PaperPositionMode','auto'); FolderName='JPEG'; mkdir(FolderName) Name=[FolderName '/Animation_']; itx=i; % disp(['itx= ' num2str(itx)]); if (itx <10) print (f1, '-djpeg100', [Name '000' num2str(itx) '.jpg'],'-r96') elseif (itx>=10 && itx <100) print (f1, '-djpeg100', [Name '00' num2str(itx) '.jpg'],'-r96') elseif (itx>=100 && itx <1000) print (f1, '-djpeg100', [Name '0' num2str(itx) '.jpg'],'-r96') else print (f1, '-djpeg100', [Name '' num2str(itx) '.jpg'],'-r96') end end pause(0.01); end 

## Second Part : Combine all the harmonics and get the square wave synthesis

shift = length(x); % This is just to save the jpeg with continuing numbers itx= 0+ shift; % which is later used for video generation for i=1:length(x) % disp([num2str(i) ' of ' num2str(Lx)]) f1=figure (2); clf; sp1=subplot(1,2,1); % -- 1st harmonic --- plot(x1,y1,'LineWidth',Lw,'Color','b'); hold on; grid on; line([0 f1cos(i)],[0 f1sin(i)],'Color','b','LineWidth',Lw,'LineSmoothing','on'); set(sp1,'Position',[0.0400 0.1800 0.4 0.677]); xlim([-2.5 2.5]); ylim([-2.5 2.5]) [xf1, yf1] = ds2nfu(sp1,f1cos(i),f1sin(i)); % Convert axes coordinates to figure coordinates for 1st axes line(f1cos(i),f1sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','b','color','b') % -- 2nd harmonic --- plot(x2+f1cos(i),y2+f1sin(i),'LineWidth',Lw,'Color','r'); hold on; line(f1cos(i)+[0 f2cos(i)],f1sin(i)+[0 f2sin(i)],'Color','r','LineWidth',Lw,'LineSmoothing','on'); [xf2, yf2] = ds2nfu(f1cos(i)+f2cos(i),f1sin(i)+f2sin(i)); % Convert axes coordinates to figure coordinates for 1st axes line(f1cos(i)+f2cos(i),f1sin(i)+f2sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','r','color','r') % -- 3rd harmonic --- plot(x3+f1cos(i)+f2cos(i),y3+f1sin(i)+f2sin(i),'LineWidth',Lw,'Color','g'); hold on; line(f2cos(i)+f1cos(i)+[0 f3cos(i)],f2sin(i)+f1sin(i)+[0 f3sin(i)],'Color','g','LineWidth',Lw,'LineSmoothing','on'); [xf3, yf3] = ds2nfu(f2cos(i)+f1cos(i)+f3cos(i),f2sin(i)+f1sin(i)+f3sin(i)); % Convert axes coordinates to figure coordinates for 1st axes line(f2cos(i)+f1cos(i)+f3cos(i),f2sin(i)+f1sin(i)+f3sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','g','color','g') % -- 4th harmonic --- plot(x4+f1cos(i)+f2cos(i)+f3cos(i),y4+f1sin(i)+f2sin(i)+f3sin(i),'LineWidth',Lw,'Color','k'); hold on; line(f2cos(i)+f1cos(i)+f3cos(i)+[0 f4cos(i)],f2sin(i)+f1sin(i)+f3sin(i)+[0 f4sin(i)],'Color','k','LineWidth',Lw,'LineSmoothing','on'); [xf4, yf4] = ds2nfu(f2cos(i)+f1cos(i)+f3cos(i)+f4cos(i),f2sin(i)+f1sin(i)+f3sin(i)+f4sin(i)); % Convert axes coordinates to figure coordinates for 1st axes line(f2cos(i)+f1cos(i)+f3cos(i)+f4cos(i),f2sin(i)+f1sin(i)+f3sin(i)+f4sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','k','color','k') title('Harmonic Circles','FontSize',Fs,'FontName','Century Gothic') set(gca,'FontSize',Fs,'FontName','Century Gothic'); %'Aharoni'); sp2=subplot(1,2,2); ylim([-2.5 2.5]); xlim([0 19]) set(sp2,'Position',[0.48 0.178200 0.49 0.680]); % Convert axes coordinates to figure coordinates for 1st axes % -- 1st harmonic --- [xg1, yg1] = ds2nfu(x(i),f1sin(i)); % -- 2nd harmonic --- [xg2, yg2] = ds2nfu(x(i),f2sin(i)); % Convert axes coordinates to figure coordinates for 1st axes % -- 3rd harmonic --- [xg3, yg3] = ds2nfu(x(i),f3sin(i)); % Convert axes coordinates to figure coordinates for 1st axes % -- 4th harmonic --- [xg4, yg4] = ds2nfu(x(i),f4sin(i)); % Convert axes coordinates to figure coordinates for 1st axes plot(x(1:i),f1sin(1:i)+f2sin(1:i)+f3sin(1:i)+f4sin(1:i),'m','LineWidth',Lw); hold on; grid on; line(x(i),f2sin(i)+f1sin(i)+f3sin(i)+f4sin(i),10,'LineStyle','-','MarkerSize',8,'MarkerFaceColor','k','color','k') ylim([-2.5 2.5]); xlim([0 19]) set(sp2,'Position',[0.48 0.178200 0.49 0.680]); [xgt, ygt] = ds2nfu(x(i),f1sin(i)+f2sin(i)+f3sin(i)+f4sin(i)); % Convert axes coordinates to figure coordinates for 1st axes annotation('line',[xf4 xgt],[yf4 ygt],'color','m','LineStyle','--','LineWidth',Lw); title('Summation of First Four Harmonics','FontSize',Fs,'FontName','Century Gothic') legend('4sin(x)/\pi + 4sin(3x)/3\pi + 4sin(5x)/5\pi + 4sin(7x)/7\pi'); xlabel('x','FontSize',Fs,'FontName','Century Gothic') set(gca,'FontSize',Fs,'FontName','Century Gothic'); %'Aharoni'); % --------------------------------------------------------------------- if (isVideOn == 1) set(gcf,'PaperPositionMode','auto'); FolderName='JPEG'; mkdir(FolderName) Name=[FolderName '/Animation_']; % disp(['itx= ' num2str(itx)]); if (itx <10) print (f1, '-djpeg100', [Name '000' num2str(itx) '.jpg'],'-r96') elseif (itx>=10 && itx <100) print (f1, '-djpeg100', [Name '00' num2str(itx) '.jpg'],'-r150') elseif (itx>=100 && itx <1000) print (f1, '-djpeg100', [Name '0' num2str(itx) '.jpg'],'-r96') else print (f1, '-djpeg100', [Name '' num2str(itx) '.jpg'],'-r96') end end itx=itx+1; pause(0.01); end