# Lysario – by Panagiotis Chatzichrisafis

"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

In [1, p. 62 exercise 3.15] it is requested to verify the ACF and PSD relationships given in [1, p. 53 eq. (3.50)] and [1, p. 54 eq. (3.51)]. read the conclusion >
In [1, p. 62 exercise 3.14] it is requested to proof prove that the autocorrelation matrix given by [1, eq. 3.46] is also positive semidefinite. This shall be done by usage of the definition of the semidefinite property of the ACF in [1, eq. 3.45]. read the conclusion >
In [1, p. 62 exercise 3.13] it is requested to prove that the PSD of a real WSS random process is a real even function of frequency. read the conclusion >
In [1, p. 62 exercise 3.12] we are asked to prove that for a WSS random process
 $r_{xx}[-k]=r^{\ast}[k].$ (1)

 $\hat{x}[n]=-\sum\limits_{k=1}^{p}\alpha_{k}x[n-k].$ (1)
Furthermore we are asked to show that the optimal prediction coefficients $\{\alpha_{1},\alpha_{2},..., \alpha_{p}\}$ are found by solving [1, p. 157, eq. 6.4 ] and the minimum prediction error power is given by [1, p. 157, eq. 6.5 ]. read the conclusion >