Editing Spectral density (section)

== Units ==
{{see also|Fourier transform#Units}}

In [[physics]], the signal might be a wave, such as an [[electromagnetic wave]], an [[sound wave|acoustic wave]], or the vibration of a mechanism. The ''power spectral density'' (PSD) of the signal describes the [[power (physics)|power]] present in the signal as a function of frequency, per unit frequency. Power spectral density is commonly expressed in [[SI units]] of [[Watt|watts]] per [[hertz]] (abbreviated as W/Hz).{{sfn | Maral | 2004}}

When a signal is defined in terms only of a [[voltage]], for instance, there is no unique power associated with the stated amplitude. In this case "power" is simply reckoned in terms of the square of the signal, as this would always be ''proportional'' to the actual power delivered by that signal into a given [[Electrical impedance|impedance]]. So one might use units of V<sup>2</sup>&nbsp;Hz<sup>−1</sup> for the PSD. ''Energy spectral density'' (ESD) would have units of V<sup>2</sup>&nbsp;s&nbsp;Hz<sup>−1</sup>, since [[energy (physics)|energy]] has units of power multiplied by time (e.g., [[watt-hour]]).{{sfn | Norton | Karczub | 2003}}

In the general case, the units of PSD will be the ratio of units of variance per unit of frequency; so, for example, a series of displacement values (in meters) over time (in seconds) will have PSD in units of meters squared per hertz, m<sup>2</sup>/Hz.
In the analysis of random [[vibration]]s, units of ''g''<sup>2</sup>&nbsp;Hz<sup>−1</sup> are frequently used for the PSD of [[acceleration]], where ''g'' denotes the [[g-force]].{{sfn | Birolini | 2007 | p=83}}

Mathematically, it is not necessary to assign physical dimensions to the signal or to the independent variable. In the following discussion the meaning of ''x''(''t'') will remain unspecified, but the independent variable will be assumed to be that of time.

=== One-sided vs two-sided ===
A PSD can be either a ''one-sided'' function of only positive frequencies or a ''two-sided'' function of both positive and [[Negative frequency|negative frequencies]] but with only half the amplitude. Noise PSDs are generally one-sided in engineering and two-sided in physics.<ref>{{Cite web |last=Paschotta |first=Rüdiger |title=Power Spectral Density |url=https://www.rp-photonics.com/power_spectral_density.html |archive-url=https://web.archive.org/web/20240415070408/https://www.rp-photonics.com/power_spectral_density.html |archive-date=2024-04-15 |access-date=2024-06-26 |website=rp-photonics.com |language=en}}</ref>