Draw the signal flow graph for a lattice filter that

Question

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 2^nd-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].