CSE 345

Solutions to Additional Problems 6.26. A signal x(t) has Laplace transform X(s) as given below. Plot the poles and zeros in the s-plane and determine the Fourier transform of x(t) without inverting X(s). (a) X(s) = s2s+5 2+1 s+6 X(s) = (s + j)(s − j) (s +3)(s +2) zeros at: ±j poles at: −3, −2 X(jω) = X(s)|s=jω = −ω2 + 1 −ω2 + 5jω + 6 Pole−Zero Map Real Axis Imag Axis −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Figure P6.26. ...