# low frequency transform

I was wondering which type of signals have bounded-support Fourier transform. e.g. their transform is limited from zero to some non-infinite frequency.

The main reason I'm into it is that in Shannon's sampling theorem, we know that for some sampling rate, reconstruction is possible without aliasing, but I guess that's only true for functions which have a limited (cut-off) frequency

• I would suggest to replace "non-infinite" by bounded-support, for improved clarity – Laurent Duval Mar 1 '18 at 11:30

## 1 Answer

Only waveforms that have infinite support in one FT domain have finite support in the other.

This implies that only impossible (in the real world) or fictitious signals comply perfectly with the sampling theorem (at a finite sampling rate). However given a non-zero noise floor (finite sized samples, quantum/Planck sampling time jitter, etc.), a common assumption is that the portion of the infinite spectrum sufficiently around or below the noise floor can be treated as zero, thus one can pretend that these signals are band-limited for practical purposes.