Consider the discrete-time system shown in the figure where

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Consider the discrete-time system shown in the figure where the impulse response of G(z) is g(0) = 0, g(1) = g(2) = 1, g(3) = g(4) =... = 0.

This system is stable for range of values of K

1. -1 , 1
  2
2. [-1 , 1]
3. - 1 , 1
  2
4. - 1 , 2
  2

Correct Option: B

G(z) = z^{– 1} + z ^{– 2}
Characteristic equation is
1 + KG (z) = 0
⇒ 1 + K (z ^{– 1} + z ^{– 2}) = 0
⇒ z² + Kz + I = 0
Using stability criteria,
| K| < 1
i.e. – 1 < K < 1