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The input-output relationship of a causal stable LTI system is given as $$y[n] =  \alpha \: y[n-1] + \beta \: x[n]$$. If the impulse response $h[n]$ of this system satisfies the condition $\sum_{n=0}^{\infty}h[n]= 2$, the relationship between $\alpha$ and $\beta$ is

  1. $\alpha = 1-\beta /2$
  2. $\alpha = 1+\beta /2$
  3. $\alpha = 2\beta$
  4. $\alpha = -2\beta$


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