What function is performed by a Fast Fourier Transform?

A Fast Fourier Transform (FFT) is a highly efficient mathematical algorithm used in Digital Signal Processing (DSP) to convert a time-domain signal, which represents amplitude over time, into a frequency-domain representation, showing amplitude over frequency. This is the process that allows a modern Software Defined Radio (SDR) to display a spectrum waterfall or panadapter. It is important to distinguish FFT from hardware conversion processes. Analog-to-digital and digital-to-analog conversions are performed by physical ADC and DAC chips, not by the FFT. Furthermore, converting signals in the reverse direction—from the frequency domain back to the time domain—is accomplished by an Inverse Fast Fourier Transform (IFFT).