%% DT Complex Exponential Demo %% Section 1 - Plot DT complex exponental in complex plane vs time % N and k may be changed to plot different signals % Plot 2 periods % Section can be run using short-key Ctrl-Enter % Define time; N=4; t_start=0; t_end = 2*N; t_res=1; t = t_start:t_res:t_end; t_ct = t_start:0.01:t_end; % contonuous time for plot of underlying complex exponential % Define period and frequency w_o = 2*pi/N; k=1; % you can choose k to be any integer and this will generate k-th harmonic of frequency k*w_0 % Define signal f = exp(k*w_o*1i*t); % dt-signal f_ct = exp(k*w_o*1i*t_ct); % ct-signal % Plot CT-complex exponential figure(1) plot3(t_ct, real(f_ct), imag(f_ct), 'LineWidth',3); hold on plot3(t_ct, real(f_ct), zeros(size(t_ct))-1, 'LineWidth',3) plot3(t_ct, zeros(size(t_ct))-1, imag(f_ct), 'LineWidth',3) % plot DT complex exponential stem3(t, real(f), imag(f), 'LineWidth',3); hold on stem3(t, real(f), zeros(size(t))-1) stem3(t, zeros(size(t))-1, imag(f)) hold off grid on view([-125 30]) xlabel('Time', 'Rotation',-30) ylabel('Real Axis', 'Rotation',10) zlabel('Imag Axis'); axis tight; %% Change View - uncomment the desired line % View Real axis only %view([0,0,1]) % View Imaginary axis only %view([0,-1,0]); % View Complex Plane %view([1,0,0]);