This fucntion is called a hybrid,
If f(t)=f(t-T) then maybe t=t-T and T=0?
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.
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
The first function is a piece-wise defined function. The second is just the first function, but shifted. If you think about signs, you'll be able to see whether the second function shifts the first one to the right or to the left.