In this problem, we consider the construction of lattice filters to implement the invers...

In this problem, we consider the construction of lattice filters to implement the inverse filter for the signal

(a) Find the values of the k-parameters k₁ and k₂ for the 2nd-order case (i.e., p = 2).

(b) Draw the signal flow graph of a lattice filter implementation of the inverse filter, i.e., the filter that outputs y[n] = Aδ[n] (a scaled impulse) when the input x[n] = s[n].

(c) Verify that the signal flow graph you drew in part (b) has the correct impulse response by showing that the z-transform of this inverse filter is indeed proportional to the inverse of S(z).

(d) Draw the signal flow graph for a lattice filter that implements an all-pole system such that when the input is x[n] = δ[n], the output is the signal s[n] given above.

(e) Derive the system function of the signal flow graph you drew in part (d) and demonstrate that its impulse response h[n] satisfies h[n] = s[n].