Script MATLAB to map the S-plane to Z-plane

The points of the s plane are related to the z plane by the function:

z=e^{st}

and below the code of a MATLAB script to map on the z plane the points of the s plane:

thetaS=0:pi/8:2*pi;
circ=exp(j*thetaS);
plot(circ);hold on
zz=ones(size(circ))*(.00001+j*0.0001)
plot([zz;circ])
axis 'square'

% Visualising the complex exponential
%                       by
%        Richard Hayes, November 2010
% Map s 2 z
%
clf;
whitebg('white');
ze=0.0001+j*0.0001;
T=1;
%   S-plane
sigma=-.3;omega=1;
s=sigma+j*omega;
 
ha4=subplot(1,2,2);
hplot4=plot(s,'or','MarkerSize',12,'MarkerFaceColor','y','LineWidth',3);hold on;
title('s-plane',...
'FontSize',20)
plot([-4+j*0.00001 0-j*4;0.5+j*0.00001 0+j*4],'k','linewidth',4)
grid
axis([-4 0.5 -4 4]);
%sgrid
 
% z-plane
ha3=subplot(1,2,1);
z=exp(s*T)+ze;
hplot1=plot(z,'or','MarkerSize',12,'MarkerFaceColor','y','LineWidth',3);hold on;
%zgrid([],[]);axis 'square';
%zgrid;axis 'square';
 
thetaS=0:pi/8:2*pi;
circ=exp(j*thetaS);
plot(circ);hold on
zz=ones(size(circ))*(.00001+j*0.0001)
plot([zz;circ])
axis 'square'
 
title('z-plane',...
'FontSize',20)
 
while 1
set(hplot4,'XData',real(s),'YData',imag(s));
 
set(hplot1,'XData',real(z),'YData',imag(z));
 
axes(ha4)
% subplot(1,2,2)
% f=imag(log(z))/2/pi;
% title(['frequency  =  ' num2str(f)],...
%         'FontSize',14)
v1 = get(ha4,'currentpoint');
s=v1(1,1)+j*v1(1,2);
z=exp(s*T);
end

Source: rghmatlabstuff.wordpress.com

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