Discrete Time Fourier Transform |In MATLAB |

  Let 𝒙(𝒏) = 𝟎. 𝟗 𝒆 𝒋𝝅𝒏 𝟑 , 𝟎 ≤ 𝒏 ≤ 𝟏𝟎. Determine 𝑿(𝒆 𝒋𝝎 ) mathematically and write the code for the signal

source Code

n = 0:10;

x = (0.9*exp((1i*pi*n/3)));

k = -300:300;

w = (pi/200)*k;

X = x*(exp(-1i*pi/100)).^(n'*k);

magX = abs(X);

angX = angle(X);

realX = real(X);

imagX = imag(X);

subplot(2,2,1);

plot(w/pi,magX, 'r');

grid on;

xlabel('Time');

ylabel('Amplitude');

title('Task2');

legend('Magnitude')

subplot(2,2,3);

plot(w/pi,angX, 'b');

grid on;

xlabel('Time');

ylabel('Amplitude');

title('Task2');

legend('Angle ')

subplot(2,2,2);

plot(w/pi,realX, 'k');

grid on;

xlabel('Time');

ylabel('Amplitude');

title('Task2');

legend(' Real  parts')

subplot(2,2,4);

plot(w/pi,imagX, 'g');

grid on;

xlabel('Time');

ylabel('Amplitude');

title('Task2');

legend('Imaginary parts')

 

Result: