Impulse response? I need a bit of help with this if anyone can?

[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 continuous system is h(t)=3e -2t-5e -4t/sup].
If the input is modeled 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 <sup>-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?</sup>

 

[lizm]

I'm doing a Music Technology course so didn't see all this maths coming at me... Thank you to anyone who can help. We have an electrical engineering lecturer and he is of the opinion that we know all of this and hasn't explained anything properly at all. I'm only a music student! So, I would really apperciate anyone who has a bit of time to go through the exercises step-by-step. Thanks

 

[lizm]

And we just got this exercise to look over and see if we have any problems...
Frequency Response
Ex. A pulse, modeled as the weighted impulse 2 [ delta] (t) , is applied to a system and produces the response y(t) = 6e ^-2t - 4e ^-3t . What is the frequency-response function of the system.
Ans. H (j [omega] ) = 5+j [omega] over (2+ j [omega] )(3+ j [omega] )

Any help?