Take the following 2 functions: (i) right-sided exponential decay. (ii) right-sided ramp.
Let's say I want to calculate the Fourier transforms of each of them. The reason for this is to calculate the energy in frequencies above w1, as a fraction of the energy in frequencies above w2, where w1>w2.
Being very unsure of myself, I go through the first 10 pages of google searches. I find that for (i), I do not need to include the implicit step response at t=0, whereas for (ii) I do need to include the implicit step response at t=0.
To complicate matters, I find that one incorrect way of proceeding with (ii) is to take a right-sided exponential decay and take the limit in the exponent coefficient tending to zero.......this is acknowledge to be incorrect as it misses the step at t=0, yet the same people who point this out do not also say that the general case of right-sided exponential decays is also wrong, for exactly the same reason.
Help!