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My goal is to express this continuous signal by using $u(t)$ (unit step) and $r(t)$ (unit ramp)basic functions

  • $u(t)$

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  • $r(t)$

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  • The signal

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So i would say that $x(t) = u(t) - r(t-1)$

Although my calculation is wrong, i have to add $+r(t-2)$ to $x(t)$ i can not quite understand why.

Why the correct answer is $x(t) = u(t) - r(t-1) + r(t-2)$ ?

Note: I'm new with with this kind of mathematics and expressions , any edit would be appriciated!

Phill Alexakis
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    I guess $r(t) = t$ for $t\ge 0$? What do you mean by "express this continuous signal" - what is this signal? Is it the combined red and blue one between 0 and 2?? – Paul Aug 28 '19 at 13:13
  • this is the $x(t)$ and i have to express it with $u(t)$ and $r(t)$ , $r(t) = t$ for $t>0$ – Phill Alexakis Aug 28 '19 at 13:38

1 Answers1

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The signal vanishes after t = 2.

To add the upward function $r(t-2)$ is to compensate, or neutralize, the downward signal $-r(t-1)$ for t > 2. Otherwise, the signal would last forever.

Quanto
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