TAREA 2

zt=[10056 18573 20195 21268 23635 23255 16675 15934 21250 24899 28636 32642 37187 41763 45789 48508 ]';
plot(zt)
n=length(zt)
zt1=[0;zt(1:n-1)]
zt2=[0;0;zt(1:n-2)]
x=[zt1 ,zt2]
b=inv(x'*x)*(x'*zt)

s=poly(0,'s')
s=s^2-b(1)*s-b(2)
raiz = roots (s)

alfa=real (raiz(1))
bet=imag (raiz(1))
r= sqrt (alfa^2+bet^2)
teta=acos(alfa/r)

t=[1:n]';
z1=(r.^t).* cos(teta*t)
z2=(r.^t).* sin(teta*t)

x=[z1 ,z2]
a=inv (x'*x)*(x'*zt)
z=a(1)*z1+a(2)*z2
plot(t,[zt z])
error1=zt-z


t=[1:0.1:n]';
z1=(r.^t).* cos(teta*t)
z2=(r.^t).* sin(teta*t)
z=a(1)*z1+a(2)*z2
plot(t,z)