How do I convolve a periodic rect function with comb function

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Mohammad
Mohammad 2022-6-10
评论： Mohammad 2022-6-10
p(x,y)=rect(2x/X)rect(2y/Y)⊗[comb(x/X)comb(y/Y)]

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Matt J
Matt J 2022-6-10
编辑：Matt J 2022-6-10
Ran in:
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

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Matt J
Matt J 2022-6-10
Ran in:
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')

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