Normalized magnitude In the MATLAB segment below we go another step: we normalize the magnitude by dividing it by N. The window is defined over 0 ≤ n ≤ (N-1) and the normalized frequency is r = ω/π. As ω varies from -π to π the normalized frequency varies from -1 to 1.

%Magnitude response rectangular window defined over n = 0 to N-1

% h(n) = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} N = 11;

b11= ones(1, 11); a=[1];

w=-pi: pi/256: pi; r = w/pi;

%

%Normalized magnitude H(ω)/N

Hw11n= freqz(b11, a, w)/N;

subplot(2, 1, 1), plot(w, abs(Hw11n)); legend (' Length = 11'); xlabel('Frequency \omega, rad/sample'), ylabel('Magnitude of H(\omega)');grid; title ('Normalized magnitude')

%

%Normalized magnitude and normalized frequency

Hr11n= freqz(b11, a, pi*r)/N;

subplot(2, 1, 2), plot(r, abs(Hr11n)); legend (' Length = 11'); xlabel('Normalized Frequency r'), ylabel('Magnitude of H(r)'); grid; title ('Normalized magnitude')

Note in the plot below that the height of the main lobe is 1 since it is normalized.

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