Every

periodic function ('wave') can be interpreted (uniquely!) as the weighted sum of elementary waves (

sines and

cosines) of different frequencies. An infinite number of frequencies may be required to describe the wave in full.

The Fourier transform is the function that describes this interpretation. It transforms a function mapping time to amplitude (running from 0 to the function's period) to the corresponding function mapping frequency to frequency strength.

Efficient methods to compute it are known as FFT ('fast Fourier transform').