| Astrophysics (Index) | About |
Spectral density is a term used in signal processing and time series analysis. Power spectral density (PSD, or power spectrum) is the distribution of power as described by the Fourier transform of the auto-correlation function of a signal. It shows the strength of the variations in power as a function of frequency. The amplitude spectral density (ASD) is the square root of the PSD, which makes differences less prominent but is scaled analogous to the data measurements. Energy spectral density (ESD) is like the PSD except that it is for a specific interval of time rather than per unit time. The terms energy and power are, in a sense, "borrowed", being analogous to how the terms are used for physical energy: one is an amount and the other a rate of the same concept over time.
The terms can be used for analysis of a continuous signal, at least in theory, but modern electronics and data collection is often digital, recording and analyzing a discrete signal formed by sampling, taking periodic samples from an incoming signal (such as a voltage output from a radio telescope antenna over time), thus using time series analysis. In the discrete case, the analysis is on a sequence of numbers, using computer algorithms. For example, for the Fourier analysis, the fast Fourier transform (FFT) (calculating the discrete Fourier transform) is likely to be used.
The term spectral density or similar terms have also been used to describe the distribution of electromagnetic radiation or other frequency-related phenomena.
The term power spectrum is also often short for angular power spectrum, something of a two-dimensional version of the power spectrum described above.