Conceptual question on FFT/IFFT (IFFT existence)
The conditions you mention only apply to the continuous-time Fourier transform, and they only have theoretical relevance. All signals occurring in engineering applications will satisfy these conditions. But if you want an example of a function with an infinite number of maxima and minima on a finite interval, here it is:

$$x(t)=\sin(1/t)$$

This function has an infinite number of minima and maxima on the interval $(0,a]$ for any real-valued $a&gt;0$.

And as for your measured signals, they are all discrete-time signals of finite length, and the above conditions do not apply. So you don't need to worry about them when using the DFT/FFT, because the DFT is defined by a finite sum, unlike the continuous-time Fourier transform, which is defined by an improper integral.