Power Spectrum

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EXPLANATION In Physics , the signal is usually a wave, such as an Electromagnetic Wave , or an Acoustic Wave . The spectral density of the wave, when multiplied by an appropriate factor, will give the Power carried by the wave, usually per unit frequency or per unit wavelength. This is then known as the power spectral density (PSD) or '''spectral power distribution''' (SPD) of the signal. The units of spectral power density are commonly expressed in Watt s per Hertz (W/Hz) or watts per nanometer (W/nm) (for a measurement versus wavelength instead of frequency). 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. DEFINITION The power spectral density, PSD, describes how the Power (or variance) of a time series is distributed with frequency. If $f(t)$ is a signal, the spectral density $\backslash Phi(\backslash omega)$ of the signal is the square of the magnitude of the Continuous Fourier Transform of the signal.

  ::<math>\int {-\infty}^\infty \left F(t) Ight^2 Dt \int_{-\infty}^\infty \Phi(\omega)\,d\omega</math>