Anyone any good at impulse response and convolution?

[liz]

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?}

 

^{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}

 

^{And we just got this exercise to look over and see if we have any problems.....}

^{Frequency Response}

^{Ex. A pulse, modelled 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?}

[Tormod]

If it is of any consolation I have a Bachelor of Music degree and was completely lost in accoustics class at college (since I had zero math experience).

 

I think they apply some kind of magic to get pure whole numbers. Or frog legs.

 

But the first one can't be that hard:

 

Ex 1) x(t)*h(t) = h(t)*x(t)

 

...that's like saying a*b = b*a, isn't it?

 

 

Good luck...

 

Tormod