I have the following function $x(t)$:
The derivative is composed of two terms, a rect and a Dirac delta. Why there is the delta Dirac? I know that the derivative of unit step is a delta Dirac, but here there isn't a step function, there is a jump discontinuity.
Thank you very much.
Best Answer
Delta appears everytime you have a jump discontinuity and you differentiate it. A mnemonic rule tells you that in this case it would be a delta concentrated in the jump times the height of the jump (provided the right sign. From left to right, if the jump is going up, it will be the case of a positive height and a positive coefficient for delta). As a particular case, if you differentiate the step function you get the simple delta function, because you have a jump with height +1 at the origin.