Fourier series of rectangular wave

%Fourier series of  rectangular wave
clc;
close all;
clear all;

j=1;
T=4;    %Time period of square wave
tau=1;  %2tau= On time of the square wave
w0=2*pi/T;
N=50;
j=1;
for k=-N:1:N
    if(k==0)
        c(j)=2*tau/T;   % fourier series coefficients of rectangular pulse
    else
        c(j)=2*sin(k*w0*tau)/(k*w0*T);
    end
   j=j+1;
end
k=-N:1:N;
subplot(2,1,1);
stem(k,c);      %plot fourier series coefficients
grid on;
xlabel('k');
ylabel('fourier series coefficient of rectangular pulse');

%%----------------------------------------------------
l=1;
time=10;
for t=-time:0.01:time
    sum=0;
    j=1;
    for k=-N:1:N
        sum=sum+c(j)*exp(i*k*w0*t); %synthesis equation
        j=j+1;
    end
    s(l)=sum;
    l=l+1;
end
t=-time:0.01:time
subplot(2,1,2);
plot(t,s);          % plot rectangular pulse
grid on;
xlabel('time');
ylabel('rectangular pulse');

QPSK modulation

%try cosine wave plot also
%a=.5;  
pi=3.14;
f=1;

x=[0 0 0 1 1 0 1 1 0 0 1 0  1 1 0 1];
nx=size(x,2);

i=1;
while i<nx+1
    t = i:0.001:i+2;
    if x(i)==0 && x(i+1)==0
        z=sin(2*pi*f*t-3*pi/4);
        dibit=0;
    elseif x(i)==0 && x(i+1)==1
        z=sin(2*pi*f*t-pi/4);
        dibit=1;
    elseif x(i)==1 && x(i+1)==0
        z=sin(2*pi*f*t+pi/4);
        dibit=2;
    else
        z=sin(2*pi*f*t+3*pi/4);
        dibit=3;
    end
    %subplot(2,1,1);
    plot(t,dibit,'r');
    %grid on;
    hold on;
    %subplot(2,1,2);
    plot(t,z);
    hold on;
    grid on;
    axis([1 20 -3 3]);
    i=i+2;

end

FM modulation

Ac=1;
fc=1;

Am=1;
fm=0.1;
kf=1.5;
B=kf*Am/fm;

t=[0:0.1:20];
ct=Ac*cos(2*pi*fc*t);
mt=Am*cos(2*pi*fm*t);
FMt=Ac*cos(2*pi*fc*t+B*sin(2*pi*fm*t));

subplot(2,2,1);
plot(mt);
ylabel('message signal');
grid on;

subplot(2,2,2);
plot(ct);
ylabel('carrier');
grid on;

subplot(2,2,3);
plot(FMt);
ylabel('FM signal');
grid on;

AM modulation

clc;
Ac=2;
fc=.9;

Am=.5;
fm=.05;
Fs=100;

ka=1;

t=[0:0.1:50];
ct=Ac*cos(2*pi*fc*t);
mt=Am*cos(2*pi*fm*t);
DSBAMt=ct.*(1+ka*mt);

subplot(2,2,1);
plot(mt);
ylabel('message signal');
grid on;

subplot(2,2,2);
plot(ct);
ylabel('carrier');
grid on;

subplot(2,2,3);
plot(DSBAMt);
ylabel('DSBAM signal');
grid on;

matlab code for digital modulation(ask, fsk and psk)

%matlab code for digital modulation(ask, fsk and psk)
pi=3.14;
f=5;
f2=10;
phi=pi;

x=[1 0 1 1 0];
nx=size(x,2);

i=1;
while i<nx+1
     t = i:0.001:i+1;
    if x(i)==1
       ask=sin(2*pi*f*t);
       fsk=sin(2*pi*f*t);
       psk=sin(2*pi*f*t);
    else
        ask=0;
        fsk=sin(2*pi*f2*t);
        psk=sin(2*pi*f*t+phi);
    end
    subplot(3,1,1);
    plot(t,ask);
    hold on;
    grid on;
    axis([1 10 -2 2]);
 
    subplot(3,1,2);
    plot(t,fsk);
    hold on;
    grid on;
    axis([1 10 -2 2]);
 
    subplot(3,1,3);
    plot(t,psk);
    hold on;
    grid on;
    axis([1 10 -2 2]);
 
    i=i+1;
end