Understanding the Ramp Function: Gate Function and Unit Step Explained"

[jesse7771]

Quick question on the ramp function, the ramp function can operate like a unit step when used in a gate function correct? Like would r(t)-r(t-2)=r(t)(r(2-t)) my teacher and book gave a really poor explanation of how the ramp function behaves, I know it only has significance when its arg>0. And that like a unit step r(-t) is a reflection across the y axis. It makes since to me that it is but I would appreciate some verification here.

 

[chiro]

Hey jesse7771 and welcome to the forums.

In terms of a general function f(-x) in compared to f(x), the function will always be reflected about the y-axis for any function not just a unit or ramp function.

In terms of those other properties, a good way to check these is to break them up into parts when the ramp starts and when it's zero and just do a piece-wise check. If you have to show these properties mathematically, you just do this symbolically.

So as an example for the step function we know that h(t-a) can be analytic when you split it up at t < a and t >= a (or whatever definition you use). If you have two functions like this you get four partitions and then you just consider all of those individually.