Frequency domain

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, <a href="/facts/Physics/a7aH2y08">physics</a>, <a href="/facts/Electronics/E4JhgISq">electronics</a>, <a href="/facts/Control_systems_engineering/5ckfXmB8">control systems engineering</a>, and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the frequency domain refers to the analysis of <a href="/facts/Mathematical_function/CdReEKCh">mathematical functions</a> or <a href="/facts/Signal_(information_theory)/41YqUJ8c">signals</a> with respect to <a href="/facts/Frequency/QUSbPaW8">frequency</a> (and possibly phase), rather than time, as in <a href="/facts/Time_series/fSXPR817">time series</a>. Put simply, a <a href="/facts/Time-domain/1w6mP2MU">time-domain</a> graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the <a href="/facts/Phase_(waves)/cpGtuVll">phase</a> of a set of <a href="/facts/Sine_wave/mD1CB09M">sinusoids</a> (or other basis waveforms) at the frequency components of the signal. Although it is common to refer to the magnitude portion (the real valued frequency-domain) as the frequency response of a signal, the phase portion is required to uniquely define the signal.
A given function or signal can be converted between the time and frequency domains with a pair of mathematical <a href="/facts/Operator_(mathematics)/1VWgEdjS">operators</a> called <a href="/facts/Transform_(mathematics)/Yr2J3o8H">transforms</a>. An example is the <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a>, which converts a time function into a complex valued sum or integral of <a href="/facts/Sine_wave/mD1CB09M">sine waves</a> of different frequencies, with amplitudes and phases, each of which represents a frequency component. The "<a href="/facts/Spectrum/wPUjkpqI">spectrum</a>" of frequency components is the frequency-domain representation of the signal. The <a href="/facts/Inverse_Fourier_transform/aM1aMkf0">inverse Fourier transform</a> converts the frequency-domain function back to the time-domain function. A <a href="/facts/Spectrum_analyzer/MatIRUbR">spectrum analyzer</a> is a tool commonly used to visualize <a href="/facts/Signal_(electrical_engineering)/41YqUJ8c">electronic signals</a> in the frequency domain.
A frequency-domain representation may describe either a static function or a particular time period of a dynamic function (signal or system). The frequency transform of a dynamic function is performed over a finite time period of that function and assumes the function repeats infinitely outside of that time period. Some specialized signal processing techniques for dynamic functions use transforms that result in a joint <a href="/facts/Time%25E2%2580%2593frequency_representation/b3BqBScJ">time–frequency domain</a>, with the <a href="/facts/Instantaneous_frequency/fJ17zuan">instantaneous frequency</a> response being a key link between the time domain and the frequency domain.

Frequency domain open-in-new

Frequency domain