Consider the separable two-dimensional Z-transform

where p₀ and p₁ are poles of X(z₁, z₂).

(a) Determine the poles and zeros of X(z₁, z₂).

(b) Carefully indicate the ROC and the location of the unit bidisc in a a (|z₁|, |z₂|) plane. According to this, does X(e^jw1 , e^jw2 ) exist?
(c) Find the inverse Z-transform of X(z₁, z₂) or x[m, n] and determine if it is absolutely summable.

Transcribed Image Text:

X(21, 2) ROC: |21| > Po, |22| > P1 2122 1– 0.5z1 – 2z2 + 212