computing matrix without using for loop

i wish to compute DFT without using a for loop so i figured to use matrix multiplication with the transformative matrix

function y = dft_mat(x,N)
for k=0:N-1
    for l=0:N-1
        w(k+1,l+1)=cos((2*pi*k*l)/N)-1i*sin((2*pi*k*l)/N);
    end
end
y=w*x';
y=y';
end

but to calculate w i ended up using some for loops anyway

is there a way to calculate w without using a for loop? or any other DFT method without using for loop?

[Bob Thompson]

You can remove one loop by applying the calculations for entire sets of l at one time.

function y = dft_mat(x,N)

l = [0:N-1];
for k=0:N-1
        w(k+1,:)=cos((2*pi*k*l)/N)-1i.*sin((2*pi*k*l)/N);
end
y=w*x';
y=y';
end

Untested, but should be about right.

Answer 1

[Steven Lord]

Compute the matrix k*l using implicit expansion with element-wise multiplication. The other operations (cos, sin, scalar multiplication, scalar division, subtraction) involved in creating w can all operate on matrices.

If you're using a release older than release R2016b, when implicit expansion was introduced, use bsxfun or repmat.

[Panda]

Yup totally forgot about element wise operations thanks a lot