How do I convolve a periodic rect function with comb function

p(x,y)=rect(2x/X)rect(2y/Y)⊗[comb(x/X)comb(y/Y)]

[Mohammad]

p(x,y) is defining a periodic function, with period X in the x direction and period Y in the y direction.

[Mohammad]

Now I need to plot p (x,y)

Answer 1

[Matt J]

X=1; Y=2;

rect=@(s) 0<=s & s<=1/2;
r=@(s) rect(mod(s+1/4,1));

[x,y]=meshgrid(-3*X:0.01:+3*X, -3*Y:0.01:+3*Y);
P=r(x/X).*r(y/Y) ;

surf(x,y,P,'EdgeColor','none');
xlabel x, ylabel y, zlabel p(x,y)
axis equal

[Mohammad]

Thanks you so much,

and also what should I do for Fourier transform of p ?

Answer 2

[Matt J]

Another possibility is to download interpMatrix

https://www.mathworks.com/matlabcentral/fileexchange/26292-regular-control-point-interpolation-matrix-with-boundary-conditions

Here is an example with a comb of sincs, rather than a comb of rects.

x=linspace(-3,+3,601); y=x;

kx=sinc( pi*x );
ky=sinc( pi*y*2 );

Ix=sum(interpMatrix(kx,'max',7,100),2);
Iy=sum(interpMatrix(ky,'max',13,50),2);

  Name        Size             Bytes  Class     Attributes

  Ix        601x1               9632  double    sparse    
  Iy        601x1               9632  double    sparse    
  x           1x601             4808  double              
  y           1x601             4808  double              

surf(x,y , Ix.*Iy','EdgeColor','none')

[Mohammad]

Thanks 🙏