Question

Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)

Answer 1

PARTA equation O 3 3 Ylz) XCz) 3z: PART B: H(z) z) x(z) Z +Z+ I Hiz) -

PART C 2 2 3Z Zeros Z, -6.5 + J o. 866 , POLE ZERo PLoT- - o.5Jo.866 J.866 Real -0.5 Z- O -jo 86 6 - 05Jo.86

PART D- る .c (n) Ces(.ao n ) = Then 식기 2 xz) +0.52 2

2 x (z) 2. 3乙 2. +0.5乙 3 z 2 3z2 Mlz) 2 3乙 3 3

PART E Srem past d Pole Zoto: Real