Using the definition given at the end of FFT document
%x is your input
x=[1 2 3 4];
fft(x) %using for comparison
Method 1
%loop approach
for j=1:numel(x)
y(j)=sum(arrayfun(@(z) x(z)*exp(-i*2*pi*(j-1)*(z-1)/numel(x)),1:numel(x)));
end
y
Method 2
%vector approach
l=length(x);
z = x*exp(-2j*pi/l*(0:l-1).'*(0:l-1))
