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Homework Help: Heavyside function help

  1. Jul 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider the triangle periodic function where x=0 @ t=0; x=2 @ t=2; x=0 @ t=4; x=2 @ t=6 and x=0 @ t=8. Let f1 be the function that agrees with f on [0,4], and is zero elsewhere. Determine f1 in terms of Heavyside step functions.


    2. Relevant equations
    Determine f1 in terms of Heavyside step functions.


    3. The attempt at a solution
    No idea....please help??!!
     
  2. jcsd
  3. Jul 9, 2010 #2

    LCKurtz

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    If u(t) is the unit step (Heaviside) function and a < b, notice that

    u(t-a) - u(t-b) is 1 between a and b and 0 elsewhere. Because of that, this difference is sometimes called a filter function. So if you multiply it by any function f(t), the resulting function will agree with f(t) on (a,b) and be 0 else where. So you can put a few of these together to build sections of your sawtooth function and have 0 outside of the filters.
     
  4. Jul 10, 2010 #3
    Ok. So you filter between the points where t=0 to t=4?
     
  5. Jul 10, 2010 #4

    LCKurtz

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    I would guess that you would be expected to filter each of the 4 pieces on that range and add them up. So you need the equation of each of the four segments for the filters.
     
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