Im trying to implement this equation in matlab

i have a matrix x[k,l] and vector k'=[-1 -5 3 4 2] and l'= [0 1 5 3 10 15 ] h'= [ 5 4 2 5 4]

how can i shift the matrix circularly by k' and l' and do the convluation with h[k' , l' ]= h' e^2*pi*k' * l' like the equation below

this is the equation that i want to implement it

y[k, l] = ∑k'=-kv to kv ∑l=0 to l' = h[k' , l' ] x[[k − k' ]N , [l − l' ]M] and and [·]N , [·]M denote modulo N and M operations

[Matt J]

Why not just implement the circulant convolution with FFTs?

Answer 1

[Matt J]

It's normally better to use FFTs for cyclic convolution, but if you insist on doing it on the non-Fourier domain, then you can use this:

function z=cyconv(x,y)
%Non-Fourier domain cyclic convolution
%
%  z=cyconv(x,y)

 siz=num2cell(size(x));

 subs=cellfun(@(n)[2:n,1:n],siz,'uni',0);

 x=x(subs{:});

 z=convn(x,y,'valid');

end

[shadi]

yes sir, i want to do by ffts how it can be please

[Matt J]

convolutionResult=ifft(fft(x).*fft(y));