1 La trasformata di Laplace

L[f(t)](s) =====∫1 2e −st f(t)dt =1 − e −2s01( [ ]e −st t=1−1 − e −2s −st=01( ∫ 1e −st dt −1 − e −2s[ e−st−s] t=2t=1)=1( 11 − e −2s s (−e−s + 1) + 1 )s (e−2s − e −s ) =11 − e −2s 1s (e−2s − 2e −s + 1) =1 11 − e −2s s (1 − e−s ) 2 =1 − e−ss(1 + e −s ) .0∫ 21)e −st dt =3. Consideriamo ora il segnale 2π-periodico denito da⎧⎨sin(t) 2kπ ≤ t ≤ (2k + 1)π, k ≥ 0f(t) =⎩0 altrimenti.11