%% L11_Windowing
%% =====================
%% Script to illustrate application of windows to reduce 
%% effect of frequency leakage in spectrum.
%%
%% Created  : 19 Aug 2005
%% Modified : 19 Aug 2005
%%
%% Copyright (c) 2005 Salman Durrani.
%% ------------------------------------------------------------

clc
clear all
close all

%% N-point DFT: Change value of N here
N=64;

%% periodic signal
n = [0:1:N-1];
x = cos(2*pi.*n./6);

%% Hamming window
w = 0.5.*(1- cos(2*pi.*n./N));

%% modified periodic signal
x_mod = x.*w;

%% Calculate DFT
X = fft(x_mod,N);
magX =  abs(X)

%% Plot w[n]
figure
stem(n,w,'filled')
xlabel('Sample n')
ylabel('w[n]')
title('Hamming Window')

%% Plot x[n] and x_mod[n]
figure
stem(n,x,'filled')
xlabel('Sample n')
ylabel('x[n]')
title('Original Signal: Fundamental Period')

figure
stem(n,x_mod,'filled')
xlabel('Sample n')
ylabel('x[n]')
title('Windowed Signal: Fundamental Period')

%% Plot DFT magnitude
figure
stem(n,magX,'filled')
xlabel('Sample k')
ylabel('|X[k]|')
title('DFT Magnitude')