Schönlieb gives an example of how Fourier transforms are used in her own area of mathematics, a field called inverse problems. She explains how images generated using magnetic resonance tomography are ...

The finite Fourier transform for periodic distributions is generalized in such a way that for every distribution f and every open interval (-a, a) there exists a Fourier series which agrees with f on ...

However, onset TRANSIENT s being APERIODIC are difficult to reproduce accurately. The more general form of transferring the frequency domain to the time domain is termed the inverse Fourier transform.