Consider a colored wide-sense stationary random signal s[n] that we desire to whiten usi...

Consider a colored wide-sense stationary random signal s[n] that we desire to whiten using the system in Figure P11.25-1: In designing the optimal whitening filter for a given order p, we pick the coefficient that satisfy the autocorrelation normal equations given by Eq. (11.34), where r_ss [m] is the autocorrelation of s[n].

It is known that the optimal 2nd-order whitening filter for s[n] is

which we implement in the 2^nd order

lattice structure in Figure P11.25-2. We would also like to use a 4th-order system, with transfer function

We implement this system with the lattice structure in Figure P11.25-3. Determine which, if any of H₄(z), k₁, k₂, k₃, k₄ can be exactly determined from the information given above. Explain why you cannot determine the remaining, if any, parameters.