%% Szereg fouriera Zad1
close all;clear all;clc;

fs=50;
t=-5:(1/fs):15;

% sygnal x(t)
xt=(abs(t)+3).*(abs(t)<=5)+0.*t.*(abs(t)>5);

Xa=zeros(size(t));
Xb=zeros(size(t));

for n=1:50
    an=(-10/(n*n*pi*pi))*(1-cos(n*pi));
    Xa=Xa+an*cos((n*pi*t)/5);
    if n==4
        Xb = Xa;
    end
end

a0 = 5.5;
Xa=(Xa+a0).*(abs(t)<=5);
Xb=(Xb+a0).*(abs(t)<=5);

plot(t,xt,'.b',t,Xa,'r',t,Xb,'g');

%% Szereg fouriera Zad2
close all;clear all;clc;

fs=50;
t=-10:(1/fs):10;

xt=(t+2).*(t>= -2 & t<=4)+0.*t.*(t>=-4 & t<=-2);

Xa=zeros(size(t));
Xb=zeros(size(t));

for n=1:100
    q=n*pi;
    an=(4/(q*q)*(cos(q)-cos(q/2)))*cos(q*t/4);
    bn=(1/q)*(4/q*sin(q/2)-6*cos(q))*sin(q*t/4);
    Xa=Xa+an+bn;
    if n==10
        Xb=Xa;
    end
end

a0=(9/4);
Xa=(Xa+a0);
Xb=(Xb+a0);

subplot(211),plot(t,xt,'k:');
subplot(212),plot(t,Xb,'r',t,Xa,'b');

%% Szereg fouriera Zad3
close all;clear all;clc;

fs=50;
t=0:(1/fs):10;

xt=0.*t.*(t>-10 & t<0)+(2*t+1).*(t>=0 & t<=2)+0.*t.*(t>2 & t<10);

Xa=zeros(size(t));
Xb=zeros(size(t));

for n=1:100
    q=n*pi;
    an=(5*sin(2*q/3)+6/q*(cos(2*q/3)-1))*cos(q*t/3);
    bn=(1-5*cos(2*q/3)+6/q*sin(2*q/3))*sin(q*t/3);
    Xa=Xa+(1/q)*(an+bn);
    if n==10
        Xb=Xa;
    end
end

a0=1;
Xa=Xa+a0;
Xb=Xb+a0;

subplot(211),plot(t,xt,'b');
subplot(212),plot(t,Xb,'g',t,Xa,'r');

%% Szereg fouriera Zad4 2018_Geofizyka_termin_1

fs=50;
t=-10:(1/fs):10;
xt=sign(t).*t.^2.*(t>=-3 & t<=3);

Xa=zeros(size(t));
Xb=zeros(size(t));

for n=1:50
    bn=36*(1-cos(n*pi))/(n*n*n*pi*pi*pi)-(18*cos(n*pi)/n*pi);
    Xa=Xa+bn*sin((n*pi*t)/3);
    if n==5
        Xb=Xa;
    end
end

Xa=Xa.*(abs(t)<=3);
Xb=Xb.*(abs(t)<=3);
t2=-3:(1/fs):3;
plot(t,xt,'g:',t,Xb,'r',t,Xa,'b');

%% Szereg fouriera Zad5 2018_Geofizyka_termin_1_G2

fs=100;
t=-3:(1/fs):3;
xt=(t+3).*(t>=-3 & t<=-1)...
    + (-2).*(abs(t)<=1)...
    + (3-t).*(t>1 &t<=3);

Xa=zeros(size(t));
Xb=zeros(size(t));

MSE=zeros(50,1);

for n=1:50
   an=(-8/n*pi)*sin(n*pi/3)-(6/n*n*pi*pi)*(cos(n*pi)-cos(n*pi/3));
   Xa=Xa+an*cos(n*pi*t/3);
   if n==25
      Xb=Xa;
   end
   MSE(n)=(1/length(t))*sqrt(sum((xt-Xa)).^2);
end

subplot(212), plot(t,xt,'r:', t,Xa,'k',t,Xb,'b');
subplot(211), plot((1:1:50),MSE);

%% Szereg fouriera Zad6 2018_Geofizyka_termin_1_G3

fs=50;
t=-10:(1/fs):10;
xt=(2+t).*(t<0)+0.*t.*(t==0)+(t-2).*(t>0);

Xa=zeros(size(t));
Xb=zeros(size(t));
L1=zeros(50,1);

for n=1:50
    bn=(2*((2-pi)*cos(n*pi)-2)/(n*pi))*sin(n*pi);
    Xa=Xa+bn;
    if n==25
       Xb=Xa;
    end
    L1(n)=(1/length(xt))*sum(abs(xt-Xa));
end

subplot(211),plot(t,xt,'r:',t,Xb,'b',t,Xa,'k');
subplot(212),plot((1:1:50),L1);