%Esercitazione richiami analisi segnali

%Definizione dei segnali
t=[1:1000];
x=cos(0.5*t);
x1=cos(0.25*t);
x2=x+x1;
w=randn(size(t));
x3=x1+w; %sommato con rumore gaussiano
x4=cos(0.5*t+w); % rumore sommato sulla fase


%DFT
DFTx=fft(x);  %NB: è un numero complesso
DFTabsX=abs(DFTx);
figure; plot(DFTabsX);
n=length(DFTx);
plot(DFTabsX(n/2-1:length(DFTx)));
DFTx1=fft(x1);
DFTabsX1=abs(DFTx1);
plot(DFTabsX1(n/2-1:length(DFTx1)));
figure;plot(DFTabsX1(n/2-1:length(DFTx1)));
figure;plot(DFTabsX1);
DFTx2=fft(x2);
DFTabsX2=abs(DFTx2);
figure;plot(DFTabsX2);
DFTx3=fft(x3);
DFTx4=fft(x4);
DFTabsX3=abs(DFTx3);
DFTabsX4=abs(DFTx4);
hold on; plot(DFTabsX3,'r'); hold on; plot(DFTabsX4,'k')
figure; plot(DFTabsX,'r'); hold on; plot(DFTabsX4,'k')
figure; plot(DFTabsX1,'r'); hold on; plot(DFTabsX3,'k')

%autocorrelazione
[acfX,lagX]=autocorr(x,100);
figure; plot(lagX,acfX,'b');hold on; plot(-lagX,acfX,'b');

[acfX2,lagX2]=autocorr(x2,100);
figure; plot(lagX2,acfX2,'b');hold on; plot(-lagX2,acfX2,'b');

[acfw,lagw]=autocorr(w,100);
figure; plot(lagw,acfw,'b');hold on; plot(-lagw,acfw,'b');

[acfX3,lagX3]=autocorr(x3,100);
figure; plot(lagX3,acfX3,'b');hold on; plot(-lagX3,acfX3,'b');

[acfX4,lagX4]=autocorr(x4,100);
figure; plot(lagX4,acfX4,'b');hold on; plot(-lagX4,acfX4,'b');

%crosscorrelazione
[ccfX2X3,lagC]=crosscorr(x2,x3,100);
figure; plot(lagC,ccfX2X3);

[ccfX1X3,lagC]=crosscorr(x1,x3,100);
[ccfXX3,lagC]=crosscorr(x,x3,100);
figure; plot(lagC,ccfX1X3);hold on; plot(lagC,ccfXX3,'r'); 


%Spettro di potenza - periodogramma
fs=512;
t2=[0:1/fs:60];
w2=randn(size(t2));
y=cos(2*pi*35*t2)+cos(2*pi*60*t2)+w2;
[Pyy,W]=periodogram(y);
[Pyy,f]=periodogram(y,hanning(length(y)),length(y),fs);

nfft=512;
[PyyW,F] = pwelch(y,hanning(nfft),0,nfft,fs);


%Cross-spettro
w3=randn(size(t2));
y2=5*cos(2*pi*35*t2)+cos(2*pi*115*t2)+cos(2*pi*60*t2)+w3;

[Pxy,Fx] = cpsd(y,y2,hanning(nfft),0,nfft,fs);

[Cxy,Fc] = mscohere(y,y2,hanning(nfft),0,nfft,fs);
figure; plot(Fx,abs(Pxy));
figure; plot(Fc,abs(Cxy));