Question

Q5. Let x(n) = T(n) be the next function: T(n) = [0.5 +0.5cos(in/N)] Where N = 50 and n = [0 : M]. Using the properties of the DTFT, determine and plot the DTFT (magnitude and phase normalized in w) of the following: 1. X(n) = T(-n). 2. X(n) = T(n) enten

using MATLAB

Answer 1

n = 0:M;

x = [1 1 1 1];

N = 50;

w2 = [0:N]*2*pi/N;

w = w2(1:end-1);

Xdtft = 0.5+0.5*cos(pi*n/N);

Xdtft1 = 0.5+0.5*cos(pi*(-n)/N);

Xdtft2 = (0.5+0.5*cos(pi*(-n)/N))*exp(j*pi*n));

plot(w/pi,abs(Xdtft))

xlabel('frequency in \pi unit','fontsize',8),

title('DTFT in (0, 2\pi)','fontsize',8)

subplot(2,1,1)

plot(T,p*180/pi)

title('Phase')

ax = gca;

ax.XTick = [15 40 60 85];

plot(w/pi,abs(Xdtft1))

xlabel('frequency in \pi unit','fontsize',8),

title('DTFT in (0, 2\pi)','fontsize',8)

subplot(2,1,2)

plot(T,p*180/pi)

title('Phase')

ax = gca;

ax.XTick = [15 40 60 85];

plot(w/pi,abs(Xdtft2))

xlabel('frequency in \pi unit','fontsize',8),

title('DTFT in (0, 2\pi)','fontsize',8)

subplot(2,1,3)

plot(T,p*180/pi)

title('Phase')

ax = gca;

ax.XTick = [15 40 60 85];