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• Spectral_density abstract "The (power) spectrum of a time-series (often, in electrical engineering applications, the voltage amplitude of a signal), describes how the variance of the data is distributed over the frequency components into which may be decomposed. This distribution of the variance may be described either by a measure or by a statistical cumulative distribution function the power contributed by frequencies from 0 up to . Given a band of frequencies , the amount of variance contributed to by frequencies lying within the interval is given by .Then is called the spectral distribution function of .Provided is an absolutely continuous function, then there exists a spectral density function . In this case, the data or signal is said to possess an absolutely continuous spectrum. The spectral density at a frequency gives the rate of variance contributed by frequencies in the immediate neighbourhood of to the variance of per unit frequency.The nature of the spectrum of a function gives useful information about the nature of , for example, whether it is periodic or not. The study of the power spectrum is a kind of generalisation of Fourier analysis and applies to functions which do not possess Fourier transforms.An analogous definition applies to a stochastic process . Furthermore, time may be either continuous or discrete.Intuitively, the spectrum decomposes the content of a signal or of a stochastic process into the different frequencies present in that process, and helps identify periodicities. More specific terms which are used are the power spectrum, spectral density, power spectral density, or energy spectral density.The variance of has units which are the square of the units of . Therefore, these are also the units of or , and so the units of the spectral density are the square of the units of per unit frequency. In the case of the voltage of an electric signal, is proportional, except that it has the wrong units, to the power of the signal (implicitly assuming a constant resistance), and so even in statistical applications which use different units, the spectral distribution function and density function are often referred to as the power spectral distribution function and the power spectral density function, although the word power is often omitted for brevity in contexts where no misunderstanding will arise.The use of the power spectrum is most important in statistical signal processing and in the branch of statistics consisting of the analysis of time-series. It is, however, useful in many other branches of physics and engineering, and may involve other units. Usually the data is a function of time but they may be a function of spatial variables instead.Blackman and Tukey gave the classic definition in 1958: ″Spectral density: A value of a function (or the entire function) whose integral over any frequency interval represents the contribution to the variance from that frequency interval.″".
• Spectral_density thumbnail Fluorescent_lighting_spectrum_peaks_labelled.svg?width=300.
• Spectral_density wikiPageExternalLink power-spectral-density.
• Spectral_density wikiPageID "202672".
• Spectral_density wikiPageRevisionID "605769384".
• Spectral_density hasPhotoCollection Spectral_density.
• Spectral_density subject Category:Frequency_domain_analysis.
• Spectral_density subject Category:Signal_processing.
• Spectral_density subject Category:Waves.
• Spectral_density type Abstraction100002137.
• Spectral_density type Event100029378.
• Spectral_density type Happening107283608.
• Spectral_density type Movement107309781.
• Spectral_density type PsychologicalFeature100023100.
• Spectral_density type Wave107352190.
• Spectral_density type Waves.
• Spectral_density type YagoPermanentlyLocatedEntity.
• Spectral_density comment "The (power) spectrum of a time-series (often, in electrical engineering applications, the voltage amplitude of a signal), describes how the variance of the data is distributed over the frequency components into which may be decomposed. This distribution of the variance may be described either by a measure or by a statistical cumulative distribution function the power contributed by frequencies from 0 up to .".
• Spectral_density label "Densidad espectral".
• Spectral_density label "Densidade espectral".
• Spectral_density label "Densité spectrale de puissance".
• Spectral_density label "Spectral density".
• Spectral_density label "Spektrale Leistungsdichte".
• Spectral_density label "Spettro di potenza".
• Spectral_density label "Trillingsanalyse".
• Spectral_density label "Widmowa gęstość mocy".
• Spectral_density label "Спектральная плотность мощности".
• Spectral_density label "スペクトル密度".
• Spectral_density label "谱密度".
• Spectral_density sameAs Spektrale_Leistungsdichte.
• Spectral_density sameAs Densidad_espectral.
• Spectral_density sameAs Densité_spectrale_de_puissance.
• Spectral_density sameAs Spettro_di_potenza.
• Spectral_density sameAs スペクトル密度.
• Spectral_density sameAs Trillingsanalyse.
• Spectral_density sameAs Widmowa_gęstość_mocy.
• Spectral_density sameAs Densidade_espectral.
• Spectral_density sameAs m.01csx9.
• Spectral_density sameAs Q1331626.
• Spectral_density sameAs Q1331626.
• Spectral_density sameAs Spectral_density.
• Spectral_density wasDerivedFrom Spectral_density?oldid=605769384.
• Spectral_density depiction Fluorescent_lighting_spectrum_peaks_labelled.svg.
• Spectral_density isPrimaryTopicOf Spectral_density.