Rational transforms Many (but by no means all) Laplace transforms of interest to us are rational functions of s(e.g, Examples #1 and #2 In genera impulse responses of lti systems described by lCCDes, where X(S=D(s), N(s),D(s)polynomials in s Roots of N(s)=zeros of X(s) Roots of D(s)=poles of X(s) Any x(t) consisting of a linear combination of complex exponentials for t>0 and for t<0(e.g, as in Example #1 and #2) has a rational Laplace transformRational Transforms • Many (but by no means all) Laplace transforms of interest to us are rational functions of s (e.g., Examples #1 and #2; in general, impulse responses of LTI systems described by LCCDEs), where • Roots of N(s) = zeros of X(s) • Roots of D(s) = poles of X(s) • Any x(t) consisting of a linear combination of complex exponentials for t > 0 and for t < 0 (e.g., as in Example #1 and #2) has a rational Laplace transform