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Find the Singularity function

  1. Mar 4, 2014 #1
    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
     

    Attached Files:

    Last edited: Mar 4, 2014
  2. jcsd
  3. Mar 4, 2014 #2
    You're right that you need four ramp functions.
    And your first three terms are correct.
     
  4. Mar 4, 2014 #3
    I made a correction to the last term, it was a typo. thou thanks scott.
     
  5. Mar 4, 2014 #4
    Singularity Function ans from professor

    So my linear systems professor had an answer that looked like this, but i really dont 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)
     

    Attached Files:

  6. Mar 5, 2014 #5
    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)
     
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