# Why peak of main-lobe in spectrum of hanning window is not equal to zero?

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Le Dung on 2 Feb 2018
Edited: Le Dung on 2 Feb 2018
Hi everyone! I'm trying to plot a spectrum of a hanning window. But when i have plotted it, i recognized that, peak of main-lobe of it is not equal to zero (image below). So, why? could you explain to me what i was wrong in my code? Thank you so much! P/s: I think peak of main-lobe in a spectrum (in dB) of window function MUST be zero.
My code:
t=0:0.001:0.5;
N=length(t);
x=1*sin(2*pi*51*t); % f of sine = 51 Hz
plot(t,x);
han=hann(N); % create a hanning window
taxis=-N/2:N/2-1; % time axis
figure;
plot(taxis,han); % Plots hanning window in time domain.
ffthan=fftshift(fft(han,N*10))/N; % calculate spectrum of windows function
faxis1= -0.5:1/N:0.5-1/N; % for case: f=-Fs/2:df:Fs/2-df => f_normalized = f/Fs
figure;
plot(20*log10(abs(ffthan))) % Plot rectangular windows in frequency domain.

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