Editing Spectral density (section)

== Related concepts ==
{{distinguish|spectral density (physical science)}}

* The ''[[spectral centroid]]'' of a signal is the midpoint of its spectral density function, i.e. the frequency that divides the distribution into two equal parts.
* {{anchor|Spectral edge frequency}} The '''spectral edge frequency''' ('''SEF'''), usually expressed as "SEF ''x''", represents the [[frequency]] below which ''x'' percent of the total power of a given signal are located; typically, ''x'' is in the range 75 to 95. It is more particularly a popular measure used in [[EEG]] monitoring, in which case SEF has variously been used to estimate the depth of [[anesthesia]] and stages of [[sleep]].{{sfn | Iranmanesh | Rodriguez-Villegas | 2017 }}{{sfn | Imtiaz | Rodriguez-Villegas | 2014}}
* {{anchor|Envelope}} A '''spectral envelope''' is the [[envelope curve]] of the spectrum density. It describes one point in time (one window, to be precise). For example, in [[remote sensing]] using a [[spectrometer]], the spectral envelope of a feature is the boundary of its [[electromagnetic spectrum|spectral]] properties, as defined by the range of brightness levels in each of the [[spectral bands]] of interest.
* The spectral density is a function of frequency, not a function of time. However, the spectral density of a small window of a longer signal may be calculated, and plotted versus time associated with the window. Such a graph is called a ''[[spectrogram]]''. This is the basis of a number of spectral analysis techniques such as the [[short-time Fourier transform]] and [[wavelets]].
* {{anchor|Phase spectrum}} A "spectrum" generally means the power spectral density, as discussed above, which depicts the distribution of signal content over frequency. For [[transfer function]]s (e.g., [[Bode plot]], [[Chirp#Relation to an impulse signal|chirp]]) the complete frequency response may be graphed in two parts: power versus frequency and [[phase (waves)|phase]] versus frequency—the '''phase spectral density''', '''phase spectrum''', or '''spectral phase'''. Less commonly, the two parts may be the [[real and imaginary parts]] of the transfer function. This is not to be confused with the ''[[frequency response]]'' of a transfer function, which also includes a phase (or equivalently, a real and imaginary part) as a function of frequency. The time-domain [[impulse response]] <math>h(t)</math> cannot generally be uniquely recovered from the power spectral density alone without the phase part. Although these are also Fourier transform pairs, there is no symmetry (as there is for the [[autocorrelation]]) forcing the Fourier transform to be real-valued. See [[Ultrashort pulse#Spectral phase]], [[phase noise]], [[group delay]].
* {{anchor|Amplitude}} Sometimes one encounters an '''amplitude spectral density''' ('''ASD'''), which is the square root of the PSD; the ASD of a voltage signal has units of V&nbsp;Hz<sup>−1/2</sup>.<ref>{{cite web
 | url = http://www.lumerink.com/courses/ece697/docs/Papers/The%20Fundamentals%20of%20FFT-Based%20Signal%20Analysis%20and%20Measurements.pdf
 | archive-url = https://web.archive.org/web/20120915030050/http://www.lumerink.com/courses/ece697/docs/Papers/The%20Fundamentals%20of%20FFT-Based%20Signal%20Analysis%20and%20Measurements.pdf
 | url-status = usurped
 | archive-date = September 15, 2012
 | title = The Fundamentals of FFT-Based Signal Analysis and Measurement
 |author1=Michael Cerna  |author2=Audrey F. Harvey
  |name-list-style=amp | year = 2000
 }}</ref> This is useful when the ''shape'' of the spectrum is rather constant, since variations in the ASD will then be proportional to variations in the signal's voltage level itself. But it is mathematically preferred to use the PSD, since only in that case is the area under the curve meaningful in terms of actual power over all frequency or over a specified bandwidth.