Homework Help: Impulse response and convolution? any help from anyone?

1. Apr 22, 2004

lizm

hey, i did my undergrad in music and english and now am lost beyond reckoning with the impulse response stuff in my postgrad. Could anyone help with these exercises? They're examples from my lecture notes and have no idea how my lecturer got the answers. Please help?

Ex.1) Show that x(t)*h(t) = h(t)*x(t)
EH? ANY IDEAS?

Ex.2) The unit response of a continous system is h(t)=3e -2t-5e -4t/sup].
If the input is modelled as x(t)= [delta](t)-2[delta](t-1)+[delta](t-2.5), find the value of the output at time=1.5s.
Ans: y(t)=0.717 at t=1.5s.

Ex.3) An electrical system has unit-impulse response h(t)= 3te -4t . If a unit step function u(t) is applied to the system, use the convolution integral to determine the value of the output after 0.25s.
Ans: 4.95 x 10 -2 V
What's the unit step function for a start??????

Ex.4) Evaluate the integral [integral infinity to minus infinity] f 1 (t)f 2 (t)dt
Where f 1 = 2sin (2000[pie]t) and f 2 (t) = [delta] (t-0.25 x 10 -3 )
Ans: 2
How do they get a pure whole number out of all those symbols?