clc
clear all
close all

% Part A
%% Plot the fundamental frequency and hear associated sound
t = 0:.1:100;
y = sin(t);
plot(t,y);
sound(y);
%% Next add the third harmonic to the fundamental, and plot/hear it.
y = sin(t) + sin(3*t)/3;
plot(t,y);
sound(y);
%% Now use the first, third, fifth, seventh, and ninth harmonics.
y = sin(t) + sin(3*t)/3 + sin(5*t)/5 + sin(7*t)/7 + sin(9*t)/9;
plot(t,y);
sound(y);

%% CODE 1
% Ideal square wave
t=-10:0.0001:10;
x=0.5*(square(t)+1);
plot(t,x)
%% CODE 2 - Square Wave
 hold on
 clc, syms n x
 L = pi; N_TERMS = input('Number of terms: '); n = 1:N_TERMS;
% % Calculating the coefficients of the Fourier Series
tic
 a0 = (1/L)*int(1, x, 0, pi);
 an = (1/L)*int(1*cos(n*x), x, 0, pi);
 bn = (1/L)*int(1*sin(n*x), x, 0, pi);
% % Plugging the coefficient values in the Fourier Series
 f = 0;
 for n = 1:N_TERMS
 f = f+ (an(n)*cos(n*x) + bn(n)*sin(n*x));
 end
toc
 fprintf('Approximation using %d terms\n', n)
 f_approx = (a0/2)+ f
 ezplot(f_approx, [-10,10])
 title('Fourier Series Approximation')
 xlabel('x')
 ylabel('F(x) approximated')
 legend('f(x)', "f'(x)");

%% CODE 3
t=-10:0.0001:10;
x=0.5*(sawtooth(t)+1);
plot(t,x)
 %% Sawtooth Wave
hold on
clc, syms n x
L = pi; N_TERMS = input('Number of terms: '); n = 1:N_TERMS;
% Calculating the coefficients of the Fourier Series
% tic
a0 = (1/L)*int(1, x, 0, pi);
an = (2/L)*int((1/L)*x*cos(2*L*n*x/L), x, 0, pi);
bn = (2/L)*int((1/L)*x*sin(2*L*n*x/L), x, 0, pi);
% Plugging the coefficient values in the Fourier Series
f = 0;
for n = 1:N_TERMS
f = f+ (an(n)*cos(n*x) + bn(n)*sin(n*x));
end
% toc
fprintf('Approximation using %d terms\n', n)
f_approx = (a0/2)+ f
ezplot(f_approx, [-10,10])
title('Fourier Series Approximation')
xlabel('x')
ylabel('F(x) approximated')