% This routine visualizes the effect of zero-padding 
% on the DTFS of a sinusoidal DT signal.

% Author:   Andreas Muschinski
% Date:     9 March 2008

clear all

% Sampling period: 1 millisecond
Ts = 0.001;

% Number of samples: L
L = 20;

% Number of padded zeros: M
M = 280;

% Total number of discrete times:
N = L+M;

% Fundamental period of continuous-time signal: 
Tc = 10.e-3;

% Fundamental frequency of CT signal:
omegac = 2*pi/Tc;

% Amplitude:
A = 2.;

% Discrete times:
n = [0:N-1]';
x = 0*n;

% Discrete frequencies:
k_orig = [0:L-1];
k_zp = [0:N-1]';

% Physical times:
tn = n*Ts;


x(1:L) = A * cos(omegac * tn(1:L));

x_orig = x(1:L);
x_zp = x;

% --------- DFTS and inverse DFTS

X_orig = fft(x_orig);
X_zp   = fft(x_zp);

omega_k_orig = (2*pi/L) * k_orig;
omega_k_zp = (2*pi/N) * k_zp;

% From 0 to pi (Nyquist interval):
omega_k_zp_Ny = omega_k_zp(1:N/2);
X_zp_Ny = X_zp(1:N/2);

[C,I] = max(abs(X_zp_Ny));
imax = I(1);
2*pi/omega_k_zp_Ny(imax)

%=================== Plot data

figure(1)
stem(n,x)
title('Zero-padded, sinusoidal DT signal')
xlabel('n')
ylabel('x[n]')

figure(2)
stem(k_orig,abs(X_orig))
title('Magnitude of DTFS of original DT signal')
xlabel('k')
ylabel('|X[k]|')

figure(3)
stem(k_zp,abs(X_zp))
title('Magnitude of DTFS of zero-padded DT signal')
xlabel('k')
ylabel('|X[k]|')

figure(4)
stem(omega_k_zp,abs(X_zp),'b')
hold on
stem(omega_k_orig,abs(X_orig),'r','LineWidth',2)
hold off
title('Magnitude of DTFS of sinusoidal DT signal (before and after zero-padding)')
legend('original DT signal','zero-padded DT signal')
xlabel('\omega_k')
ylabel('X[k]')