How Do You Express a Piecewise Function Using Singularity Functions?

[E&H12]

I was given the problem to:
express the following signal in terms of the singularity function

g(t)= t-1, 1<t<2
1, 2<t<4
4-t, 4<t<5
0, otherwise


I graphed this function it is attached in below.

My final answer for this function is

g(t)= r(t-1)-r(t-2)-r(t-4)+r(t-5).

Is this answer correct? Thank You

 

[.Scott]

You're right that you need four ramp functions.
And your first three terms are correct.

 

[E&H12]

I made a correction to the last term, it was a typo. thou thanks scott.

 

[E&H12]

Singularity Function ans from professor

So my linear systems professor had an answer that looked like this, but i really don't agree with this answer. Will someone please explain which one is correct? Where did my professor get those last terms from? (it does not make sense to me)

 

[.Scott]

The original specification includes: 4-t for 4<t<5
So this would range from 4-4 to 4-5 or 0 to -1. So your original graph is wrong and the teacher is correct.
(Sorry, I didn't catch that one either)
Still, your original graph is useful as an intermediate result. Your teach called your function G3 and his/her work is in agreement with your corrected result:
g3(t)= r(t-1)-r(t-2)-r(t-4)+r(t-5)

But then we need to drop that 4<t<5 segment so we need a -u(t-4)+u(t+5).
The whole thing becomes, just as your teacher reported:
g(t)= r(t-1)-r(t-2)-r(t-4)+r(t-5)-u(t-4)+u(t+5)