Complex sentence: Fourier analysis converts a signal from its original domain (often time or space) to the frequency domain (or wavenumber) and vice versa; an FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.
Split into simpler sentences: Fourier analysis converts a signal from its original domain (often time or space) to the frequency domain and vice versa. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.