Named after Joseph Fourier, the french mathematician who proposed that mathematical functions can be decomposed into a sum of sine functions in a 1807 paper on heat transfer [2].
WSJT-X makes extensive use of a tool from Fourier analysis called the Discrete Fourier Transform (DFT).
This transform takes time domain representations of signals (what you would see on an oscilloscope) and converts them to frequency domain representations (what you would see on a spectrum analyser).
Computing the DFT of a sequence of samples is computationally expensive, and therefore the DFT was not widely
used until 1965 when a method for rapidly computing the DFT become widely known after it was disclosed in a
paper by Cooley and Tukey [3].
This method for computing the DFT is now known as the fast Fourier transform (FFT) algorithm.
WSJT-X uses a particular implementation of the FFT algorithm called
"The Fastest Fourier Transform in the West" (FFTW),
that was originally developed in the mid-1990s by Frigo and Johnson while they were students at MIT
[4].
The following example illustrates how the DFT can be used to convert a time domain representation of a signal
to a frequency domain representation using the Python scipy implementation of the FFT algorithm.