very confused with the impulse response and convolution. Can anyone help?

[Guest 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?}

 

^{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?}

[dryan]

I don't really feel like reading all that stuff right now, but it looks convoluted to me...was that the question?

[Daniel]

I am not going to do the questions.

 

Convolution because multiplication in the S domain. If you can laplace transform the two functions to be convolved, then you can multiply them and inverse transform to get the convolved result.

 

The first exercises just shows the linear properties of the functions..............homogeneity. Sort of like 2 * 3 = 3 * 2

 

Unit step function is a function which is 0 before a certain time, then goes to 1 instantaneously from that time onwards. If you plot it, it should look like a step. Step response is the response of a system to a step input.

 

A delta function is just a spike at a certain time, and 0 everywhere else. If you multiply it with something, you will only get the value of that something at the location of the spike. Think about it, if you multiply by the delta function which is 0 everywhere else except for one certain point, then you will only get a value at that point (and 0 everywhere else).

 

I recommend that you do a lot more reading.