## EE 451

MATLAB code for Example 9.1.4, from Orfanidis

```fs=10e3;    % Sampling frequency
T=1/fs;     % Sampling period
f1=2e3;     % Frequencies of three sinusoids
f2=2.5e3;
f3=3e3;
w = 0:pi/1000:pi;  % Frequencies to calculate DFT

figure(1)

L = 10;            % Define L
n=0:L-1;
x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T)+cos(2*pi*f3*n*T); % Calcular x(n)*w(n)
X=0;               % Calculate X(w)
for k=0:L-1
X = X + x(k+1)*exp(-j*w*(k));
end
subplot(221)
plot(w/pi,abs(X))
axis([0 1 0 50])
title('Rectangular Window -- L = 10')

h = hamming(L);      % Find Hamming window
Xh=0;                % Xh(w) = DFT [x(n)*h(n)]
for k=0:L-1
Xh = Xh + x(k+1)*h(k+1)*exp(-j*w*(k));
end
subplot(222)
plot(w/pi,abs(Xh))
axis([0 1 0 50])
title('Hamming Window -- L = 10')

L = 20;
n=0:L-1;
x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T)+cos(2*pi*f3*n*T);
X=0;
for k=0:L-1
X = X + x(k+1)*exp(-j*w*(k));
end
subplot(223)
plot(w/pi,abs(X))
axis([0 1 0 50])
title('Rectangular Window -- L = 20')

h = hamming(L);
Xh=0;
for k=0:L-1
Xh = Xh + x(k+1)*h(k+1)*exp(-j*w*(k));
end
subplot(224)
plot(w/pi,abs(Xh))
axis([0 1 0 50])
title('Hamming Window -- L = 20')

figure(2)

L = 40;
n=0:L-1;
x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T)+cos(2*pi*f3*n*T);
X=0;
for k=0:L-1
X = X + x(k+1)*exp(-j*w*(k));
end
subplot(221)
plot(w/pi,abs(X))
axis([0 1 0 50])
title('Rectangular Window -- L = 40')

h = hamming(L);
Xh=0;
for k=0:L-1
Xh = Xh + x(k+1)*h(k+1)*exp(-j*w*(k));
end
subplot(222)
plot(w/pi,abs(Xh))
axis([0 1 0 50])
title('Hamming Window -- L = 40')

L = 100;
n=0:L-1;
x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T)+cos(2*pi*f3*n*T);
X=0;
for k=0:L-1
X = X + x(k+1)*exp(-j*w*(k));
end
subplot(223)
plot(w/pi,abs(X))
axis([0 1 0 50])
title('Rectangular Window -- L = 100')

h = hamming(L);
Xh=0;
for k=0:L-1
Xh = Xh + x(k+1)*h(k+1)*exp(-j*w*(k));
end
subplot(224)
plot(w/pi,abs(Xh))
axis([0 1 0 50])
title('Hamming Window -- L = 100')

```