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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spectral density ： ウィキペディア英語版 Spectral density The power spectrum of a time series $x(t)$ describes how the variance of the data $x(t)$ is distributed over the frequency domain, into spectral components which the series $x(t)$ may be decomposed. This distribution of the variance may be described either by a measure $\backslash mu$ or by a statistical cumulative distribution function $S(f)=$the power contributed by frequencies from 0 up to $f$. Given a band of frequencies $[a,b)$, the amount of variance contributed to $x(t)$ by frequencies lying within the interval $[a,b)$ is given by $S(b)-S(a)$.〔or, equivalently, by the measure of that interval, $\backslash mu([a,b))$.〕 Then $S$ is called the spectral distribution function of $x$. Provided $S$ is an absolutely continuous function,〔or, equivalently, $\backslash mu$ is absolutely continuous with respect to Lebesgue measure.〕 then there exists a spectral density function $S\text{'}$. In this case, the data or signal is said to possess an absolutely continuous spectrum. The spectral density at a frequency $f$ gives the rate of variance contributed by frequencies in the immediate neighbourhood of $f$ to the variance of $x$ per unit frequency. The nature of the spectrum of a function $x$ gives useful information about the nature of $x$, 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 $X(t)$. 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 $x$ has units which are the square of the units of $x$. Therefore, these are also the units of $\backslash mu$ or $S$, and so the units of the spectral density are the square of the units of $x$ per unit frequency. In the case of the voltage of an electric signal, $x^2$ 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. == Explanation == Any signal that can be represented as an amplitude that varies with time has a corresponding frequency spectrum. This includes familiar concepts such as visible light (color), musical notes, radio/TV channels, and even the regular rotation of the earth. When these physical phenomena are represented in the form of a frequency spectrum, certain physical descriptions of their internal processes become much simpler. Often, the frequency spectrum clearly shows harmonics, visible as distinct spikes or lines at particular frequencies, that provide insight into the mechanisms that generate the entire signal. In physics, the signal is usually a wave, such as an electromagnetic wave, random vibration, or an acoustic wave. The ''power spectral density'' (PSD) of the signal, when multiplied by the appropriate factor, describes the power contributed to the wave, by a frequency, per unit frequency. Power spectral density is commonly expressed in watts per hertz (W/Hz). For voltage signals, it is customary to use units of V2 Hz−1 for the PSD and V2 s Hz−1 for the ESD (''energy spectral density''). Often it is convenient to work with an ''amplitude spectral density'' (ASD), which is the square root of the PSD; the ASD of a voltage signal has units of V Hz−1/2.〔(【引用サイトリンク】 The Fundamentals of FFT-Based Signal Analysis and Measurement )〕 For random vibration analysis, units of ''g''2 Hz−1 are frequently used for the PSD of acceleration. Here ''g'' denotes the g-force. Although it is not necessary to assign physical dimensions to the signal or its argument, in the following discussion the terms used will assume that the signal varies in time. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spectral density」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.