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Expressing a function as Heaviside function

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I have a question: given a piecewise function, f(t)= {t when t<=0 ,0 when 0<t<=1, 1-t when t>1. How do express it as a Heaviside function?
I have tried to do the solution which is : f(t)= (1-t)*H(t-1)+t*H(t). Here I have considered two non-zero portions of f(t), which are t and 1-t. Is that right? Please let me know about my attempt.
 

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vela
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I have a question: given a piecewise function, f(t)= {t when t<=0, 0 when 0<t<=1, 1-t when t>1. How do express it as a Heaviside function?
I have tried to do the solution which is : f(t)=(1-t)*H(t-1)+t*H(t). Here I have considered two non-zero portions of f(t), which are t and 1-t. Is that right? Please let me know about my attempt.
No, it's not correct. Consider when t=2, for instance. You'd get

f(2) = (1-2) H(2-1) + 2 H(2) = (-1) H(1) + 2 H(2) = 1

whereas according to original the definition of f(t), f(2) should equal -1. You can see from this example the problem arises because the t*H(t) term contributes when it no longer should. Can you see how to modify your function to get that to go away?
 

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