I got curious based on this question [here](https://dsp.stackexchange.com/questions/10148/power-spectral-density-vs-energy-spectral-density), but basically, is there ever a real-life signal that exists where its Fourier transform does not exist? If a signal is not finite energy, then its Fourier Transform does not exist, so what might be an example, (if any), of such a signal in real-life?