% M-file for Sec2 Lec 03.
%
% Plots for Figure 61 of PW

p1 = 1;
if( p1 == 1 ) 
    % Generate gp(t) = 1-phi^2/(1+phi^2-2pji*cos(t))
    phi = 0.9;
    arg = [-pi:0.01:pi];
    gp = (1-phi^2)./(1+phi^2-2*phi*cos(arg));
    % gp,m=1+2*sum+n=1^m[(phi^2*cos(nt)]
    m = 4; l=length(arg);
    c = zeros(32,l);
    for n = 1:32
        c(n,:) = phi^n*cos(n*arg);
    end
    % Now sum the functions to different levels
    gp04 = 1 + 2*sum(c([1:4],:));
    h1 = figure(1); set(h1,'Position',[100 300 750 160],'PaperPositionMode','auto');
    plot(arg,gp,'b',arg,gp04,'r'); axis tight; 
    title('Approximation to (1-\phi^2)./(1+\phi^2-2\phi cos(arg)) with m=4, \phi=0.9');
    print -dpng S2L03_gp04.png
    % Now sum the functions 8 level
    gp08 = 1 + 2*sum(c([1:8],:));
    h2 = figure(2); set(h2,'Position',[120 280 750 160],'PaperPositionMode','auto');
    plot(arg,gp,'b',arg,gp08,'r'); axis tight; 
    title('Approximation to (1-\phi^2)./(1+\phi^2-2\phi cos(arg)) with m=8, \phi=0.9');
    print -dpng S2L03_gp08.png
    % Now sum the functions to 16 levels
    gp16 = 1 + 2*sum(c([1:16],:));
    h3 = figure(3); set(h3,'Position',[140 260 750 160],'PaperPositionMode','auto');
    plot(arg,gp,'b',arg,gp16,'r'); axis tight; 
    title('Approximation to (1-\phi^2)./(1+\phi^2-2\phi cos(arg)) with m=16, \phi=0.9');
    print -dpng S2L03_gp16.png
    % Now sum the functions to 32 levels
    gp32 = 1 + 2*sum(c([1:32],:));
    h4 = figure(4); set(h4,'Position',[160 240 750 160],'PaperPositionMode','auto');
    plot(arg,gp,'b',arg,gp32,'r'); axis tight; 
    title('Approximation to (1-\phi^2)./(1+\phi^2-2\phi cos(arg)) with m=32, \phi=0.9');
    print -dpng S2L03_gp32.png

end

p2 = 1;
if( p2 == 1 ) 
    % Generate Gaussion pair:
    sig = 1;
    t = [-4:0.02:4]; f=t; 
    gt1 = 1/sqrt(2*pi*sig^2)*exp(-(t.*t)/(2*sig^2));
    Gf1 = exp(-2*pi*f.*f*sig^2);
    h1 = figure(5); set(h1,'Position',[100 300 750 160],'PaperPositionMode','auto');
    plot(t,gt1,'r',f,Gf1,'k'); axis tight; 
    title('Gaussian with transform \sigma=1');
    print -dpng S2L03_gt1.png    

    sig = 4;
    gt4 = 1/sqrt(2*pi*sig^2)*exp(-(t.*t)/(2*sig^2));
    Gf4 = exp(-2*pi*f.*f*sig^2);
    h2 = figure(6); set(h2,'Position',[120 280 750 160],'PaperPositionMode','auto');
    plot(t,gt4,'r',f,Gf4,'k'); axis tight; 
    title('Gaussian with transform \sigma=4');
    print -dpng S2L03_gt4.png    
end