1. Show that a system specified by the equation y[n]−y[n−1] = x[n] is BIBO unstable. 2. Explain with reason(s) whether the following systems are (1) linear or nonlinear, (2) time invariant or time...

2. Explain with reason(s) whether the following systems are (1) linear or nonlinear, (2) time invariant or time variant, and (3) causal or noncausal.

(a) an ideal backward difference system defined by the input-output relationship

y[n] = x[n] − x[n − 1]

(b) an ideal forward difference system de- fined by the input-output relationship

y[n] = x[n + 1] − x[n]

(c) a moving-average system defined by the input-output relationship

(d) an accumulator defined by the inputoutput relationship