%ALIAS illustre l'effet de l'aliasing spatial dans les plans x,t et kx,om
% voir : http://jmmeost.free.fr/Sismique/isis.html
% fig1 = http://jmmeost.free.fr/Sismique/alias.gif  

clear all

V0 = 1000;

dx = 50;   nx = 40; xx = 0:dx:(nx-1)*dx; dcx = 1/dx/nx; cxn = 1/2/dx;
dt = .01;  nt = 50; tt = 0:dt:(nt-1)*dt; df = 1/nt/dt; fn = 1/2/dt;
[XX, TT] = meshgrid(xx,tt);

f0 = 5; nh = 5;
al = 30*pi/180; p0 = 2*sin(al)/V0;

figure(1), clf, colormap('copper')

for ih = 1:nh;
fh = f0*ih;
pxt = cos(2*pi*fh*(p0*XX-TT));

subplot(5,2,1+2*(ih-1)), hold on
imagesc([0 nx*dx],[0 nt*dt],pxt)
plot([0 nx*dx],[0 nx*dx]*p0,'r','Linewidth',2)
if ih == 1
legend(['{\alpha} = ' num2str(al*180/pi) '°'])
title(['COS(KX*X-OM*T), DX = ' num2str(dx) ' M, DT = ' num2str(dt) ' S, V = ' num2str(V0) ' M/S'])
else
plot([nx*dx 0],nt*dt+[nx*dx 0]*(p0-2*cxn/fh),'b',[0 nx*dx],[0 nx*dx]*(p0-2*cxn/fh),'b','Linewidth',2)
legend(['{\alpha} = ' num2str(al*180/pi) '°'],['{\alpha}al = ' num2str(asin((p0-2*cxn/fh)*V0/2)*180/pi,'%2.0f') '°'])
end
set(gca,'Xlim',[0 nx*dx],'Ylim',[0 nt*dt],'YDir','reverse','DataAspectRatio',[1000 1 1])
xlabel('X (M)'), ylabel('T(S)')

subplot(5,2,2+2*(ih-1)), hold on, grid on
imagesc(zeros(nt/2,nx))
plot(fh*p0,fh,'ro','Markerface','r')
plot([0 cxn],[0 cxn]/p0,'r',[-cxn cxn],cxn/p0+[0 2*cxn]/p0,'r',[-cxn cxn],3*cxn/p0+[0 2*cxn]/p0,'r','Linewidth',2)
plot(2*cxn+[0 cxn],[0 cxn]/p0,'r--',2*cxn+[-cxn cxn],cxn/p0+[0 2*cxn]/p0,'r--',2*cxn+[-cxn cxn],3*cxn/p0+[0 2*cxn]/p0,'r--','Linewidth',2)
plot(-2*cxn+[0 cxn],[0 cxn]/p0,'r--',-2*cxn+[-cxn cxn],cxn/p0+[0 2*cxn]/p0,'r--',-2*cxn+[-cxn cxn],3*cxn/p0+[0 2*cxn]/p0,'r--','Linewidth',2)
legend(['F = ' num2str(fh) ' HZ'],'Location','NorthWest')
if (ih == 1)
title(['FN = 1/2/DT = ' num2str(fn) ' HZ, CXN = 1/2/DX = ' num2str(cxn) ' /M'])
else
plot(fh*p0-2*cxn,fh,'bo','Markerface','b')
plot([0 fh*p0-2*cxn],[0 fh],'b','Linewidth',2),
end
set(gca,'Xlim',[-3*cxn 3*cxn],'Ylim',[0 fn],'YDir','reverse')
plot([cxn cxn],[0 fn],'k',-[cxn cxn],[0 fn],'k','Linewidth',2)
xlabel('CX (1/M)'), ylabel('F(HZ)')
end