Image:DFT approximation to Hilbert filter.png

N = 512;
h = zeros(1,N/2);
odd = 1:2:N/2;
 
for n = odd
    h(n) = 2/(pi*n);
end
 
H =  [-i*ones(1,N/2) i*ones(1,N/2)];
g = real( ifft(H) );
g = g(2:end);
 
figure
semilogy(odd,g(odd),'r',odd,h(odd),'b')
 
xlabel('n (odd values only)')
xlim([1 256])
set(gca,'XTick',1:50:251)
ylabel('impulse response (for n > 0)')
title('DFT_{512} approximation to Hilbert Filter')
 
text(200,.006,'2/(\pi n)','color','b','FontSize',14)
text(120,.0004,'DFT approximation  \rightarrow','color','r','FontSize',14)