The spectral density of a fluorescent light
as a function of optical wavelength shows peaks at atomic transitions, indicated by the numbered arrows.
The power spectrum
of a time series
the distribution of power
into frequency components composing that signal.
According to Fourier analysis
any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise
) as analyzed in terms of its frequency content, is called its spectrum
When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density
. More commonly used is the power spectral density
(or simply power spectrum
), which applies to signals existing over all
time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating
over the time domain, as dictated by Parseval's theorem
The spectrum of a physical process
often contains essential information about the nature of
. For instance, the pitch
of a musical instrument are immediately determined from a spectral analysis. The color
of a light source is determined by the spectrum of the electromagnetic wave's electric field
as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform
, and generalizations based on Fourier analysis. In many cases the time domain is not specifically employed in practice, such as when a dispersive prism is used to obtain a spectrum of light in a spectrograph
, or when a sound is perceived through its effect on the auditory receptors of the inner ear, each of which is sensitive to a particular frequency. Read more...