Hi all. I can't remember what this type of function is called for the life of me, so sorry for being vague in the description. This is just part of a much bigger question and for some reason I get stuck at this part...

I have two functions:

f(t) = 1 for 0 < t < 1 and -1 for 1<t<2
f(t-T) = 1 for 0 < t-T < 1 and -1 for 1<t-T<2

so far so good.
I'm supposed to know that f(t) = f(t-T) = 1 for 0<t<1-T, but how do I know this? I've not done a problem like this in like 3 years, so please give me some pointers.

This fucntion is called a hybrid,

If f(t)=f(t-T) then maybe t=t-T and T=0?

Originally Posted by pickslides
This fucntion is called a hybrid,

If f(t)=f(t-T) then maybe t=t-T and T=0?
Yeah, that's what I first thought. The problem is that I start with f(t) then add the last term -T to get f(t-T). I really need it to become f(t)=f(t-T) = 1 for 0 < t < (1-T) to integrate this function properly.

If I try it backwards: f(t) - f(t-T) = 0 so (0<t<1) - (0<t-T<1) = 0
What is allowed to do here? I see I can't take each term like: (0-0<t-t+T<1-1).
How do I make the range of f(t) "fit" into f(t-T) using math, basically.

I'm thinking I can use some way to say that (0<t) and that t<(1-T) and just putting them together without breaking the mathematical logic.

This is in a Signal & Circuit theory course at uni, all my math is done, but this type of problem is something that does not show up that often :P