In each case xt represents the input and yt represents the

Question

Question: In each of the following cases, state whether or not the continuous-time system is

(i) Linear;

(ii) Time-invariant;

(iii) Stable. and

(iv) Causal.

In each case x(t) represents the input and y(t) represents the corresponding output of the system. Provide a brief justification either in the form of mathematical equations or statements in the form of complete. correct. English sentences. Remember. in order to show that the system does not have the pmperty, all you have to do is give an example input whose output does not satit the condition of the property.

(a) An exponentiation system is defined by the input/output relation

y(t) = exp{x(t + 2)} = e^{x(t + 2)}

(b) A phase modulator is a system whose input and output satisfy a relation of the form

y(t) = cos[ω_ct + x(t)]

(c) An amplitude modulator is a system whose input and output satisfy a relation of the form

y(t) = [A + x(t)]cos(ω_ct)

(d) A system that takes the even part of an input signal is defined by a relation of the form

y(t) = εv{x(t)} = x(t) + x(-t)
                               2