The transfer function of a digital system is given by:; where a2 is real.The transfer function is BIBO stable if the value of a2 is:a)andminus;1.5b)andminus;0.75c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer?

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The transfer function of a digital system is given by:

; where a₂ is real.
The transfer function is BIBO stable if the value of a₂ is:

a)
−1.5
b)
−0.75
c)
0.5
d)
1.5

Correct answer is option 'C'. Can you explain this answer?

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The transfer function of a digital system is given by:; where a2 is re...

Transfer function of the digital system is,

The stability of a two-pole system can be investigated by a stability criterion method called “schr−cohn” stability test”.

In this approach the reflection coefficients K₁and K₂ are to be calculated from the denominator pdynomial. This method states that a second order system is stable if its reflection coefficients |k₁| <1 and |k2| <1. It is also given that,

These two conditions are satisfied by 0.5
Note: An alternative approach to solve this problem is trial and error method. Each option is substituted for 'a₂'in the system function and poles are to be calculated. The value 'a₂' which gives both the poles inside the unit-circle is the suitable „a2?. Here a2 = 0.5 satisfies the
condition.

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The transfer function of a digital system is given by:; where a2 is real.The transfer function is BIBO stable if the value of a2 is:a)−1.5b)−0.75c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer?

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