Number of state variables of discrete-time system, described by

\(y[n] - \frac{3}{4}y[n - 1] + \frac{1}{8}y[n - 2] = x[n]\) is

This question was previously asked in

ESE Electronics 2010 Paper 1: Official Paper

Option 1 : 2

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

**Concept:**

Number of state variables = order of the system

= number of independent energy storage elements

= number of poles of the system.

**Analysis:**

\(y[n] - \frac{3}{4}y[n - 1] + \frac{1}{8}y[n - 2] = x[n]\)

Taking Z transform we get:

Y(Z) - 0.75 Z^{-1} Y(Z) + 0.125 Z^{-2} Y(Z) = X(Z)

Y(Z) [ 1 - 0.75 Z-1 + 0.125 Z-2 ] = X(Z)

\({Y(Z) \over X(Z)} = \frac{1}{0.125 Z^{-2} - 0.75 Z^{-1} + 1}\)

The number of poles = 2

Hence, number of state variables = 2