Question

Consider the signal f(t)= $\large e^{-t}(sin5t+sin40t) 0\leqslant t\leqslant pi$

ps:

Filter this signal with the Butterworth filter (i.e., compute (f * h)(i) forO š I

Answer 1

Solution .- Given the Signal is, (L) = e-.sinらt + sinat tsint t sinyot Filter +is n sional utterusorth Signal We need t check our assumptions f Y L and hlt T bounds of th artifical,and in the case f h, arbitahu The convolution --C two-tun ction s flt ) and he) i the conte of an inverse Laplace +vans-form f he Product thtran sforms

es pe cively is ff e vemove the bounds of fit 〉and het) -at.-t//a-, )s、hLt).cosLL) A3e 1 2 1- on-a 160

a 2 a- a 1 a2 2a26 a2-2a 16o a2- 2a+26 a16o

A C- a41601