 The subsequent development of the field is known as harmonic analysis, and is also an early instance of representation theory.The first fast Fourier transform (FFT) algorithm for the DFT was discovered around 1805 by Carl Friedrich Gauss when interpolating measurements of the orbit of the asteroids Juno and Pallas, although that particular FFT algorithm is more often attributed to its modern rediscoverers Cooley and Tukey.In signal processing, the Fourier transform often takes a time series or a function of continuous time, and maps it into a frequency spectrum.