%% L10_DFT
%% =====================
%% Script to illustrate how to:-
%% (i) calculate DFT and 
%% (ii)investigate relationship between DFT and DTFT.
%%
%% Created  : 17 Aug 2005
%% Modified : 17 Aug 2005
%%
%% Copyright (c) 2005 Salman Durrani.
%% ------------------------------------------------------------

clc
clear all
close all

n=[0 1 2 3];
x=[0 1 0 0];

%% ------------------------------------------------------------
%% Find FFT
N=4;
X = fft(x);

%% Find DTFT
num=[0 1];
den=1;
w = [0:0.01:2*pi];
[H,W]=freqz(num,den,w);

%% Plot Mags (without scaling x axis)
subplot(2,2,1)
stem(n,abs(X),'filled')
hold on
plot(W,abs(H),'k-')

xlabel('Sample k')
ylabel('|X[k]|')
legend('DFT Magnitude','DTFT Magnitude')

%% Plot Phases (without scaling x axis)
subplot(2,2,3)
stem(n,angle(X)*180/pi,'filled')
hold on
plot(W,angle(H)*180/pi,'k-')

xlabel('Sample k')
ylabel('< X[k] (degs)')
legend('DFT Phase','DTFT Phase')

%% Plot Mags (scaling x axis)
subplot(2,2,2)
stem(n,abs(X),'filled')
hold on
plot(W*N/(2*pi),abs(H),'k-')

xlabel('Sample k')
ylabel('|X[k]|')
legend('DFT Magnitude','DTFT Magnitude')

%% Plot Phases (scaling x axis)
subplot(2,2,4)
stem(n,angle(X)*180/pi,'filled')
hold on
plot(W*N/(2*pi),angle(H)*180/pi,'k-')

xlabel('Sample k')
ylabel('< X[k] (degs)')
legend('DFT Phase','DTFT Phase')