Instrument2PowerSpectralDensity
This program computes the power spectral density (PSD) for all data fields in an instrument file. The PSD is computed using Lomb's method. For each arc and each frequency $f$, a sinusoid is fit to the data \[ l_i = a \cos(2\pi f t_i) + b \sin(2\pi f t_i) + e_i \] The PSD for this frequency is then computed by forming the square sum of adjusted observations: \[ P(f) = \sum_i \hat{l}^2_i. \] The resulting PSD is the average over all arcs. For regularly sampled time series, this method yields the same results as FFT based PSD estimates.
A regular frequency grid based on the longest arc and the median sampling is computed. The maximum number of epochs per arc is determined by \[ N = \frac{t_{\text{end}} - t_{\text{start}}}{\Delta t_{\text{median}} } + 1, \]the Nyquist frequency is given by \[ f_{\text{nyq}} = \frac{1}{2\Delta t_{\text{median}}}. \] If it is suspected that inputfileInstrument contains secular variations, the input should be detrended using InstrumentDetrend.
See also Instrument2CovarianceFunctionVCE, CovarianceFunction2PowerSpectralDensity, PowerSpectralDensity2CovarianceFunction.
| Name | Type | Annotation |
|---|---|---|
outputfilePSD | filename | estimated PSD: column 0: frequency vector, column 1-(n-1): PSD estimate for each channel |
inputfileInstrument | filename |