Solution 2.9.2.3 f(t)=A[1(t);1(t ;T)] + B [1(t; T); 1(t; 2T)] Then F(s) = LfA[1(t)g;LfA1(t ;T)]g+ LfB1(t ;T)g;LfB1(t ; 2T)g = A s ; Ae ;Ts s + Be ;Ts s ; Be ;2Ts s = A(1;e ;Ts )+B(e ;Ts ; e ;2Ts ) s Check: F(s) = Z T 0 Ae ;st dt + Z 2T T Be ;st dt = ;A s h e ;st i T 0 ; B s h e ;st i 2T T = A(1; e ;sT )+B(e ;sT ; e ;2sT ) s 1