The linear constant coefficient difference equation $$y\left( n \right) - \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right) + \frac{1}{3}x\left( {n - 1} \right)$$ lead to
A. $$\frac{{Y\left( Z \right)}}{{X\left( Z \right)}} = \frac{{1 + \frac{1}{3}{Z^{ - 1}}}}{{1 + \frac{1}{2}{Z^{ - 1}}}}$$
B. $$\frac{{Y\left( Z \right)}}{{X\left( Z \right)}} = \frac{{1 - \frac{1}{3}{Z^{ - 1}}}}{{1 - \frac{1}{2}{Z^{ - 1}}}}$$
C. $$\frac{{Y\left( Z \right)}}{{X\left( Z \right)}} = \frac{{1 - \frac{1}{3}{Z^{ - 1}}}}{{1 + \frac{1}{2}{Z^{ - 1}}}}$$
D. $$\frac{{Y\left( Z \right)}}{{X\left( Z \right)}} = \frac{{1 + \frac{1}{3}{Z^{ - 1}}}}{{1 - \frac{1}{2}{Z^{ - 1}}}}$$
Answer: Option D
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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