Question

If of the input signal X(t) and output signal yl to a continuous - time linear time - invariant system - Y(t) = 5 to xc ej elt- el de o find the impluse response of the system hat) o If the input signal is x (t) = f(t) - f (t-1) find the output signal y ct)

Answer 1

YLt) = J (7) e-It- dr 0 impulse response 3) (T) = S(V). = y(t) = f sa e lt -Iton de Tors we know that f(t-a) a (t) = (a) ft-a) fit-ajat = i. for act .. . y(t) = 1 e(t) dri ③ 900 2 .1-e! since system pis Linear time invariant ylt. Vailt) = yill). y(t) laict-ta) = Y;lt-to)

.:-) y It) x(t) = d.lt) (EU) 94) RạU = (( - ) so when inputs are ricts thalt). outputs will be yi (t) tyz(t) because system is linear when dilt) = f(t) Yilt = i-et for to When Aalt) = f(t-1) Y₂ (t) = 1- When (t) = nilts - Aalt) then Yg (t) = y, iti ga lts. = let (i-e (t-1) e-(t-) et for to for to