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Signals and Systems - Engineering

Q1:

If function f(t) has an initial value f(0-) at t = 0-, the Laplace transform of is

A sF(s) - f(0-)

B sF(s) + f(0-)

C s2F(s) - f(0-)

D s2F(s) + f(0-)

ANS:A - sF(s) - f(0-)

£f(t) = £-1F(s) = f(t) £[a f1(t) + bf2(t)] = aF1(s) + bF2(s) where £[f(t - T)] = e-sT F(s) £[e-at f(t)] = F(s + a) Initial value theorem Final value theroem Convolution Integral where t is dummy variable for t.