Matlab Hann window task

clear all; close all; clc;  %Cleaning up


%Task:
%In Matlab, plot the Hann- and Hamming window in the frequency domain with
%window length N=41 by numerically calculating the Fourier transform.

%Notes:
%This code only features the Hann window for simplicity
%Demonstration function for comparison:
L = 41;
wvtool(hann(L))

%Task Properties
N=41;           %Data points
SEGMENTS=1000;   %Segments for the transform. Minimum of 200. Around 4101 yields no -Inf through testing.


%The Hann function, time domain
a=0.5;  %Hann window specifics
b=0.5;
t=0:N-1;    %Time axis
w=a-b*cos(2*pi*t/(N-1));    %The function

% plotting
subplot(2,1,1)
stem(t,w)
xlabel('N')
grid on

%The Fourier Transformation, frequency domain
v=0:1/(SEGMENTS-1):1;   % Time axis with 1000 points
W=fft(w,SEGMENTS);      % Fourier transform with 1000 points
Wabs=abs(W);            % Take absolute value
Wabs=mag2db(Wabs);      % and convert to dB

% plotting
subplot(2,1,2)
plot(v,Wabs);
ylabel('dB')
xlabel('Normalized frequency')
grid on
axis([0 1/2 -100 50])