This problem illustrates the development of digital filter structures using Horner?s rule for polynomial evaluation. To this end consider the polynomial,

p(x) = a_px_p + a_p-1x^p-1 + . . . + a₁x + a₀

which computes p(x) with the minimum cost of p multiplications and p additions.

(a) Draw the structures corresponding to the factorizations and determine the system function, number of delay elements, and arithmetic operations for each structure

(b) Draw the Horner structure for the following linear-phase system:

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(a) H; (z) = bo(1 + bị 2-'(1 + bzz¬'(1 + bzz-1)) H(2) = bo(z- + (b)z-2 + (bzz+ b3))) (b) 3. ++*)a H(z) = 2-| aæo + kal