# Converting to unit impulse function

mathrocks
I was wondering how do you go about converting something like tri(t-1) to the unit impulse function. How do you convert any function to a unit impulse function?

More specifically I'm trying to find the Laplace transform of x(t)=[tri(t-1)]e^(-3t)

And I was told you have to convert the tri(t-1) part to a unit impulse and then it become easy.

Staff Emeritus
I take it "tri" is a triangle function with ramp up from 0 to some value, then ramp down?

In that case, start with a ramp t, then figure what must be added to ramp down.

It's a bit like making a square/rectangular function by superimposing step functions, e.g. u(t) - u(t-1).

mathrocks
Astronuc said:
I take it "tri" is a triangle function with ramp up from 0 to some value, then ramp down?

In that case, start with a ramp t, then figure what must be added to ramp down.

It's a bit like making a square/rectangular function by superimposing step functions, e.g. u(t) - u(t-1).

So would it be ramp(t)+ramp(-t-1)

If that's the case, then how would you find the Laplace of that when it replaces tri(t-1)?