Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...

Speaking non-technically, a time domain graph shows how a signal changes over time, whereas a frequency domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency domain representation also includes information on the phase shift that must be applied to each frequency in order to be able to recombine the frequency components to recover the original time signal. Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ...

The frequency domain relates to the Fourier series by decomposing a signal into an infinite or finite number of frequencies. Fourier series are a mathematical technique for analyzing an arbitrary periodic function by decomposing the function into a sum of much simpler sinusoidal component functions, which differ from each other only in amplitude and frequency. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

Magnitude and phase

In using the Laplace, Z-, or Fourier transforms, the frequency spectrum is complex and describes the frequency magnitude and phase. In many applications, phase information is not important. By discarding the phase information it is possible to simplify the information in a frequency domain representation to generate a frequency power spectrum. A spectrum analyser is a device that displays the power spectrum. // Real numbers The magnitude of a real number is usually called the absolute value or modulus. ... Look up Phase in Wiktionary, the free dictionary Phase may refer to: Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter Phase (waves), the time position (or angle in the complex plane) within a cycle of a periodic waveform... The power spectrum is a plot of the portion of a signals power (energy per unit time) falling within given frequency bins. ... A spectrum analyzer is a device used to examine at the spectral composition of some electrical, acoustic or optical waveform. ...

Real-life frequency domain example

A biological system that operates in the frequency domain is the auditory system, in which the basilar membrane of the inner ear is able to perform a power spectrum decomposition of incoming sound waves. The result is that we are able to hear a collection of different frequencies played together as a collection of separate notes, rather than simply a complicated noise. The auditory system is the sensory system for the sense of hearing. ... Cross section of the cochlea. ... A human girls ear An ear is the organ used by an animal to detect sound waves. ...

See also

• Frequency spectrum
• Power spectrum
• Spectrum analyzer