clear;

N_signal=1024;
% generating two-sin signal
for (k=1:1:N_signal)
          garm(k)=1*sin(2*pi/20*(k-1))+2*sin(2*pi/50*(k-1));
    
end;

plot(garm);

% ARMA process generating
ar(1)=0.5*randn(1);
ar(2)=0.9*ar(1)+0.5*randn(1);

for (i=3:1:N_signal)
    ar(i)=0.9*ar(i-1)-0.7*ar(i-2)+0.5*randn(1);
end;



signal=garm+1*ar;

plot(signal);



signal_c=signal-mean(signal,2);

[acf,lags]=xcorr(signal_c,signal_c);

plot(lags,acf)


N=size(lags,2);
dt=1;
% from Lab 1 - caluclation of frequencyes
for(j=1:1:N)
      if(j==1)
        t(j)=0;
        omega(j)=0;   

      elseif(j<=N/2+1)
        t(j)=N*dt/(j-1); 
        omega(j)=2*pi/t(j); 

      elseif(j>N/2+1)
        t(j)=N*dt/(N-j+1);
        omega(j)=-2*pi/t(j);
       
      end;
      
      
 end;
spectr_dens=sqrt(fft(acf)/N_signal);
plot(t,abs((spectr_dens))) %Power Spectral Dencity over periods (not frequencies)