TEST BANK FOR Discrete Time Signal processing 3rd Edition By Alan V. Oppenheim, Ronald W. Schafer Converted

2.1. (a) T(:z:[n]) = g[nl*l • • Stable: Let 1*11 $ M then IT[*] I :;; lg[n]IM. So, it is stable if lg[n]l is bounded. • Causal: y,[n] = g[n]z1[n] and 112[n] = g[n]:z:2[n], so if :z:,[n] = :z:2[n] for all n < no, then y,[n] = 112[n] for all n <no, and the system is causal. • Linear: So tbis is linear. • Not time-invariant: which is not TI. T(a:z:1[n] + b:z:2[n]) = g[n](=1 [n] + bz2[n] = og[n]:z:1[n] + bg[n]:z:2[n] = oT(:z:1[n]) + bT(z2[n]) T(:z:[n - no]) = g[n]:z:[n - ...