Hanning window Frequency Domain Graph

Hello,

I have calculated the time domain of the hanning window through the formula.

But now I have to find the frequency domain by using fft and fft shift which i have calculated but I want to know is this graph correct or not?

M = 40;
n = -M / 2: M / 2;
window = 0.5 + 0.5 * cos (2 * pi * n / M);
figure;
plot (n, window);

L = length (window); 
NFFT = 1024;
X1 = fftshift (fft (window, NFFT) / length (window));
Freq = (-NFFT / 2: NFFT / 2-1) / NFFT;     % Frequency vector

figure; 
plot (Freq, X1 (1: length (Freq)) / max (X1), 'r' );

Answer 1

[Pratyush Roy]

The graph for frequency response is correct. In case you want to generate a plot for magnitude response in decibels, make the following changes to the code:

Y1 = X1 (1: length (Freq)) / max (X1);
mag_dB =  10*log10(Y1);
plot(Freq,mag_dB);

The following link to the documentation might be helpful ofr generating frequency response for Hanning window using the 'hann' function available in the Signal Processing Toolbox in MATLAB.

https://www.mathworks.com/help/signal/ref/hann.html

Answer 2

[Leo Dokoza]

What does "M" stand for? Could you explain your code?