Consider the QMF filterbank shown in Figure P4.50: The input–output relationshi...

Consider the QMF filterbank shown in Figure P4.50:

The input–output relationship is Y(z) = T (z)X(z), where

and E₀(z²), E₁(z²) are the polyphase components of H₀(z).

Parts (a) and (b) are independent.

(a) Explain whether the following two statements are correct: (a1) If H₀(z) is linear phase, then T(z) is linear phase.

(a2) If E₀(z) and E₁(z) are linear phase, then T(z) is linear phase.

(b) The prototype filter is known, h₀[n] = δ[n] + δ[n − 1] + 1 4 δ[n − 2]:

(b1) What are h₁[n], g₀[n] and g₁[n]?

(b2) What are e₀[n] and e₁[n]?

(b3) What are T (z) and t [n]?