The difference equation for a system is given by

y(n + 2) + y(n + 1) + 0.16 y(n) = x(n + 1) + 0.32 x(n)

The transfer function of the system is

This question was previously asked in

ESE Electronics 2012 Paper 1: Official Paper

Option 1 : \(\frac{(z+0.32)}{(z^2+z+0.16)}\)

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

**Concept:**

Time-shifting:

If X(z) is a z transform of x(n), then the z transform of x(n – n0) is,

\(x\left( {n - {n_0}} \right) \leftrightarrow {z^{ - {n_0}}}X\left( z \right)\)

**Analysis: **

The difference equation:

y(n + 2) + y(n + 1) + 0.16 y(n) = x(n + 1) + 0.32 x(n)

z^{2} Y(z) + z^{1} Y(z) + 0.16 Y(z) = z^{1} X(z) + 0.32 X(z)

\(\frac{Y(z)}{X(z)}=\frac{z^{1} + 0.32}{z^{2}+z^{1}+0.16}\)

∴ Option 1 is the correct answer