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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

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Answer (Detailed Solution Below)

Option 1 : 2
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Detailed Solution

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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

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