Comparison of two rectangular windows of lengths 11 and 31 In the MATLAB code below we go other step: we normalize the value by dividing it by N. The window is described over 0 ≤ n ≤ (N-1) and the normalized frequency is r = ω/π. As ω taken from -π to π the normalized frequency varies from -1 to 1.
%Magnitude response rectangular window defined over n = 0 to N-1
% Comparison of two rectangular windows of lengths 11 and 31
N1 = 11; b11= ones(1, N1); N2 = 31; b31= ones(1, N2); a=[1];
w=-pi: pi/512: pi; r = w/pi;
%
%Length 11, normalized magnitude and normalized frequency
Hr11n= freqz(b11, a, pi*r )/N1;
subplot(2, 1, 1), plot(r, abs(Hr11n)); legend ('Length = 11');
xlabel('Normalized Frequency r'), ylabel('Magnitude of H(r)'); grid
%
%Length 31, normalized magnitude and normalized frequency
Hr31n= freqz(b31, a, pi*r)/N2;
subplot(2, 1, 2), plot(r, abs(Hr31n)); legend ('Length = 31');
xlabel('Normalized Frequency r'), ylabel('Magnitude of H(r)'); grid
Only the first side lobe is of concern since all the other side lobes are smaller. From the plot below the maximum of the first side lobe is a little over 20% of the height of the main lobe in both windows.
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