% C. Talarico
% simusoids.m

clear all; close all; clc;

f  = 100;   % 100 Hz
T  = 1/f;   % 10 ms
A = 20e-3;  % 20mV 
t = 0:1e-6:40e-3;
wt = 2*pi*f.*t;
vin = A*cos(wt);

B  = A/2;
td = 2e-3;        % time delay
pd = 2*pi*td/T;   % phase shift 
fprintf('time delay = %0.2g [ms] \n', td*1e3);
fprintf('time delay is %0.2g%% of the period (T = %0.2g [ms]) \n'...
    ,100*td/T, T*1e3);
fprintf('phase shift in deg = %0.2g [degree] \n', 360*td/T);
fprintf('phase shift in rad = %0.2g pi [rad] \n', pd/pi);
vout = B*cos(wt-pd);
% double check time delay ( <-> phase shift) finding the value of t and wt 
% for which vout has its first peak
idx = find(vout == B, 1, 'first');
td  = t(idx)
phd = wt(idx)*180/pi 

figure(1);
plot(t*1e3, vin*1e3, 'linewidth', 2, 'color', 'k');
xlabel('time [ms]', 'fontsize', 16);
ylabel('voltage [mV]','fontsize', 16);
ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
hold on;
plot(t*1e3, vout*1e3, 'linewidth', 2, 'color', 'b', 'linestyle', ':');
legend('vin','vout','location','bestOutside');
title('voltage vs. time', 'Fontsize', 18, 'fontname', 'monospace');

figure(2);
plot(wt, vin*1e3, 'linewidth',2, 'color','m');
xlabel('\omegat [rad]', 'fontsize', 16);
ylabel('Voltage [mV]','fontsize', 16);
title('voltage vs. phase', 'fontsize',18, 'FontName','monospace');
xlim([0 8*pi]);
ax = gca;
set(ax,'Fontsize',16, 'Fontweight', 'Normal');
set(ax, 'xtick', [0, pi, 2*pi, 3*pi, 4*pi, 5*pi, ... 
    6*pi, 7*pi, 8*pi])
set(ax, 'xtickLabel', {'0', 'p', '2p', '3p','4p', '5p', '6p','7p', ...
    '8p'}, 'fontname','Symbol');
hold on;
plot(wt,vout*1e3, 'linewidth',2, 'linestyle',':','color','r');
leg = legend('vin','vout','location','bestOutside');
set(leg, 'fontname','Monospace');