1. A certain LTI system has system mapping S satisfying S(x) = Shift3(x) h0 x for all x 2 Dh0 , where h0 is a decent signal and Dh0 is the set of all decent signals x for which h0 x exists. You can be certain that (i) If h0(t) = e3t for all t 2 R and x 2 Dh0 , then Shift13(x) 2 Dh0 (ii) If x has finite duration, then x 2 Dh0 (iii) If h0(t) = e3tu(t) for all t 2 R and x is a decent right-sided signal, then x 2 Dh0 (iv) The system is causal when h0(t) = 0 for all t