Correlations,contrasts, and components: Fourier analysis in a more familiar terminology

The Fourier transform partitions the energy in a waveform into the sum of the energies of simpler components. This process is the same as the partitioning of variance into linear contrasts and is a way of measuring the correlation between the waveform and each member of a family of prototype model waveforms. Such a partitioning will often, but not always, result in a meaningful decomposition of the original waveform.