Solve the following problems.
- Find the DTFT of the following input function
- Implement the following Matlab script to simulate the DTFT with magnitude and phase response of the following function.
Here, that converts above expression into DTFT of a function.
clf; clc;
% Compute the frequency samples of the DTFT
N = 512
w = -4*pi:8*pi/N:4*pi; % simulation period in frequency domain -4pi to pi
num = [ ]; % define numerator polynomial coefficients in this vector
den = [ ]; % define denominator polynomial coefficients in this vector
h = freqz(); % use freqz()with above arguments to find DTFT in Matlab
% Plot the DTFT
subplot(2,1,1)
plot(w/pi, ); % plot the real value of the DTFT
grid on;
title('Real part of H(e^{j\omega})')
xlabel('\omega /\pi');
ylabel('Amplitude');
subplot(2,1,2)
plot(w/pi, );grid on; % plot the imaginary value of the DTFT
title('Imaginary part of H(e^{j\omega})')
xlabel('\omega /\pi');
ylabel('Amplitude');
figure;
subplot(2,1,1)
plot(w/pi, );grid on ; % calculate the magnitude spectrum of DTFT
title('Magnitude Spectrum |H(e^{j\omega})|')
xlabel('\omega /\pi');
ylabel('Amplitude');
subplot(2,1,2)
plot(w/pi, );grid on; % calculate the phase spectrum of DTFT
title('Phase Spectrum arg[H(e^{j\omega})]')
xlabel('\omega /\pi');
ylabel('Phase in radians');
- Attach both the figures here.