FFT is heavily used in communication, radar or computer systems. For example OFDM (orthogonal frequency division multiplexing) is developed based on IFFT and FFT. Since Python is most common used scientific programming language beside Matlab, I would like to present some information about FFT and using it in Python.
This blog post (https://jakevdp.github.io/blog/2013/08/28/understanding-the-fft/) includes the basics of the FFT and very clear comparison of it to DFT. Another blog post (https://www.ritchievink.com/blog/2017/04/23/understanding-the-fourier-transform-by-example/) which includes a very good example of the FFT. This page (https://plot.ly/python/fft-filters/) has FFT filters using Python. An OFDM example which utilizes FFT and IFFT in Python is presented here (https://dspillustrations.com/pages/posts/misc/python-ofdm-example.html) .
An extra link: (http://www.music.helsinki.fi/tmt/opetus/uusmedia/esim/index-e.html) in which you can find some .wav sound examples to process using FFT. An application of short-term FFT on sounds: short term
Sound Processing with Short Time Fourier Transform