Find the Laplace transform of the following signals and in each case determine the corresponding region of

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Find the Laplace transform of the following signals and in each case determine the corresponding region of convergence:

(a) the signal x(t) = eˆ’αtu(t) ˆ’ eαt u( ˆ’ t) when (i) α > 0, (ii) α †’ 0,

(b) a sampled signal

N-1 ()Σε-ίδ ( = ) x1 (t) = 2η n=0

(c) the €œstairs to heaven€ signal

s(0) %3D У и(t — п) Σα п30

(d) the sinusoidal signal v(t) = [cos(2(t ˆ’ 1)) + sin(2Ï€ t)] u(t ˆ’ 1),

(e) the signal y(t) = t2eˆ’2tu(t)using that x(t) = t2u(t) has X(s) = 2/s3.

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