%[**Please copy and paste below code to Matlab inorder to compute the power of two square wave signals f(t) and g(t) from their complex Fourier series with n= 10 for two cases: 1. A period of 2 seconds and a pulse width of 1 second. 2. A period of 4 seconds and a pulse width of 1 second. and edit : Line 11: Enter a value for the period of the square waves. Line 13: Enter a value for the pulse width of the square waves. Line 118: Enter a MATLAB expression to calculate the power of the f(t) signal. Line 120: Enter a MATLAB expression to calculate the power of the g(t) signal. **]%

% Plot amplitude and phase spectra of square waves offset from each other

% by time a/2.

close all; % close all open figures. Comment out to leave figures from previous runs open

%% CHANGE VALUES OF a,T

% ---------- INPUT NEEDED ---------- %

% Period (sec)

T = 2; % CHANGE THIS VALUE

% Peak width (sec)

a = 1; % CHANGE THIS VALUE

% max value of n include in the discrete complex spectra's double sided sum

n_max = 10; % Optional: mess around with different values of n_max as well

% ----------------------------------- %

% Angular fundamental frequency (rad/s)

omega0 = 2*pi/T;

%% Time-domain Square waveforms

% Square waveform f(t): break into sections (overlap at endpoints ok for

% plotting)

tsq1 = linspace(-T, -T+a, 31)'; % 31-element x column vector

gsq1 = ones(size(tsq1)); % vector of ones the same size as xsq1

tsq2 = linspace(-T+a, 0, 31)';

gsq2 = zeros(size(tsq2));

tsq3 = linspace(0, a, 31)';

gsq3 = ones(size(tsq3));

tsq4 = linspace(a, T, 31)';

gsq4 = zeros(size(tsq4));

tsq5 = linspace(T, T+a, 31)';

gsq5 = ones(size(tsq5));

% Assemble all these sections into one square wave x vector (xsq) and y

% vector (ysq), both column vectors

tsq = [tsq1; tsq2; tsq3; tsq4; tsq5];

gsq = [gsq1; gsq2; gsq3; gsq4; gsq5];

% Plot of square wave f(t)

fig_f = figure; % create a new figure window and assign to handle fig_f

set(gcf,'Position',[18 1 560 800]); % prescribe figure position and dimensions

subplot(3,1,1) % multiple plots in one figure. 3x1 array of figures, plot in spot 1

% plot original square wave with black line, line width 2

plot(tsq-a/2,gsq,'-b','LineWidth',2); % note that f(t) = g(t - a/2)

grid on; hold on

xlabel('t'); ylabel('f(t)'); % always label axes

title('Square wave f(t) in time domain');

set(gca,'FontSize',18,'LineWidth',3,'FontWeight','bold',...

'TickLength',[0.025 0.025]); % Make axes legible

axis([-1.5*T 1.5*T -0.25 1.25]) % prescribe axis limits

axf = gca; % save handle of time-domain waveform plot for f(t)

% Plot of square wave g(t)

fig_g = figure;

set(gcf,'Position',[632 1 560 800]); % prescribe figure position and dimensions

subplot(3,1,1)

plot(tsq,gsq,'-r','LineWidth',2);

grid on;

xlabel('t'); ylabel('g(t)');

title('Square wave g(t) in time domain');

set(gca,'FontSize',18,'LineWidth',2,'FontWeight','bold',...

'TickLength',[0.025 0.025]);

axis([-1.5*T 1.5*T -0.25 1.25]);

axg = gca;

%% COMPLEX SPECTRA OF f(t), g(t)

n = (-n_max:n_max)'; % harmonic index n, column vector

% f(t)***************************** amplitude spectrum*******************

fampl = a/T*abs(sinc(n*pi*a/T));

% f(t) phase spectrum

fphase = zeros(size(n));

% g(t) ************************amplitude spectrum************************

gampl = a/T*abs(sinc(n*pi*a/T));

% g(t) amplitude spectrum

gphase = -n*pi*a/T;

% Plot f(t) spectra

figure(fig_f); % plot next commands on f(t) figure

% f(t) amplitude spectrum

subplot(3,1,2)

stem(n*pi*a/T, fampl,'LineWidth',1.5)

xlabel('Frequency n\pia/T (rad/s)'); ylabel('|c_n|');

title('Amplitude spectrum')

set(gca,'FontSize',18,'LineWidth',2,'FontWeight','bold',...

'TickLength',[0.025 0.025]);

% f(t) phase spectrum

subplot(3,1,3)

stem(n*pi*a/T, fphase,'LineWidth',1.5)

xlabel('Frequency n\pia/T (rad/s)'); ylabel('\phi_n');

title('Phase spectrum')

set(gca,'FontSize',18,'LineWidth',2,'FontWeight','bold',...

'TickLength',[0.025 0.025]);

% Plot g(t) spectra

figure(fig_g); % plot next commands on f(t) figure

% g(t) amplitude spectrum

subplot(3,1,2)

stem(n*pi*a/T, gampl,'LineWidth',1.5)

xlabel('Frequency n\pia/T (rad/s)'); ylabel('|c_n|');

title('Amplitude spectrum')

set(gca,'FontSize',18,'LineWidth',2,'FontWeight','bold',...

'TickLength',[0.025 0.025]);

% g(t) phase spectrum

subplot(3,1,3)

stem(n*pi*a/T, gphase,'LineWidth',1.5)

xlabel('Frequency n\pia/T (rad/s)'); ylabel('\phi_n');

title('Phase spectrum')

set(gca,'FontSize',18,'LineWidth',2,'FontWeight','bold',...

'TickLength',[0.025 0.025]);

%% Power of signal

% ---------- INPUT NEEDED ---------- %

% Calculate the power of the signal f(t)

power_f = abs(famp1).^2;

% Calculate the power of the signal g(t)

power_g = gamp1gamp1.^2;

% Output results to screen

fprintf(' For square waves of pulse width: %3.2f sec, period %3.2f sec:',a,T);

fprintf(' \tPower of signal f(t): %5.4e',power_f);

fprintf(' \tPower of signal g(t): %5.4e ',power_g);

% ---------------------------------- %