Given a system described by a function H that maps input signals x to output signals y. (a) Without assuming linearity or time invariance, write down the mathematical definition for a causal system. (6m) (b) State whether the system is causal (and justify your answer): if the output is given by [H(x)](t) = e 5) x (t). -a (t+5) if the output is given by [H(x)](t) = e-itx (t + 5). (c) Suppose that a system has impulse response h. Use the definition in part (a) to derive the conditions that h has to satisfy for the system to be causal. (7m) (d) Give a mathematical definition of a BIBO stable system. (4m) (e) If H is given by (2m) (2m) (H(x)) (t) = f'x(r) dr