Frequency domain

Frequency domain is the coordinate system in which a signal or system is described by its frequency components rather than by its values at successive instants of time. It is the dual space to the time domain, and the gateway between them is the Fourier transform. In the frequency domain, a system's behavior is characterized by how it amplifies, attenuates, or phase-shifts each frequency component of an input signal — a description that is often far simpler than the corresponding time-domain differential equations.

The frequency domain is the natural habitat of linear time-invariant systems. In this domain, convolution becomes multiplication, and the complex dynamics of a system collapse into a single function of frequency. The spectral density of a signal reveals structure invisible in the time domain, from resonant peaks of mechanical oscillators to rhythmic patterns of neural populations.