Here is a YouTube video about the discovery of discrete and fast Fourier transforms, and is part of a growing collection of videos I have found to be useful for understanding software defined radio. It is a well written and expertly explained account of how nuclear scientists seeking to examine seismometer spectra found a way to time domain data into frequency domain data.
It is interesting, as the discovery was made in secret - during the period of rampant superpower competition in nuclear weapons testing. However, the Discrete and Fast Fourier transforms were found by Gauss in the year 1805, but the knowledge was lost until modern experts found them in his notes. Gauss was two years ahead of Fourier and more than a century ahead of the modern mathematician who worked out the Fast Fourier Transform. Incredible.
This tutorial uses a video titled, "The Algorithm That Transformed The World," and is free education you can watch, which will help you deepen your knowledge and be better prepared for licence exams, schoolwork, or operating radio equipment.