engineering recuitment GATE EE 2023-24 Test Series Signals and Systems Z Transform Z Transform From Difference Equation
The input-output relationship of a causal stable LTI system is given as
y[n] = α y[n – 2] + β x[n]
If the impulse response h[n] of this system satisfies the condition \(\mathop \sum \limits_{n = 0}^\infty h\left[ n \right] = 4,\) the relationship between α and β is
1
4α – β = 4
2
4α + β = 4
3
α = 4β
4
α = -4β