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A stable discrete-time LTI system is described by the following difference equation: y[n] − y[n − 1] + Cy[n − 2] = x[n] ,where C is a real number. Determine the range of C so that (a) the system is causal; (b) the system is anti-causal; (c) the system is non-causal (i.e., it has a two-sided impulse response).

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A stable discrete-time LTI system is described by the following difference equation:y[n]

− y[n − 1] + Cy[n − 2] = x[n]

,where C is a real number. Determine the range of C so that

(a) the system is causal;

(b) the system is anti-causal;

(c) the system is non-causal (i.e., it has a two-sided impulse response).

 
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