Fourier transform - plane - square

maxima_fourier-transform-plane-square

Fourier transform - 2D

integrate(integrate(h(x,y)*exp(-%i*2*%pi*(u*x+v*y)),x,-inf,inf),y,-inf,inf);

square

h(x,y):= ( unit_step( x+(1/2) ) - unit_step( x-(1/2) ) )
                 * ( unit_step( y+(1/2) ) - unit_step( y-(1/2) ) );
plot3d(h(x), [x,-10,10],[y, -10, 10]);

Example:

integrate(integrate(1*exp(-%i*2*%pi*(u*x+v*y)),x,-1/2,1/2),y,-1/2,1/2);
realpart(%);
plot3d(%, [u,-4,4],[v,-4,4],[grid,25,25]);

maxima_fourier-transform-plane-square