psd (version 0.4-1)

pilot_spec: Calculate the pilot power spectral densities.

Description

This PSD -- the pilot spectrum -- is used as the starting point for the adaptive estimation routine.

Usage

pilot_spec(x, x.frequency = 1, ntap = 7, remove.AR = 0, plot = FALSE,
  verbose = FALSE, ...)
## S3 method for class 'default':
pilot_spec(x, x.frequency = 1, ntap = 7, remove.AR = 0,
  plot = FALSE, verbose = FALSE, ...)

Arguments

x

vector; the data series to find a pilot spectrum for

x.frequency

scalar; the sampling frequency (e.g. Hz) of the series

ntap

scalar; the number of tapers to apply during spectrum estimation

remove.AR

scalar; the max AR model to be removed from the data.

plot

logical; should a plot be created?

verbose

logical; should messages be given?

...

additional parameters passed to psdcore

Value

• An object with class 'spec', invisibly. It also assigns the object to "pilot_psd" in the working environment.

Removing an AR effect from the spectrum

If remove.AR > 0 the argument is used as AR.max in prewhiten, from which an AR-response spectrum is calculated using the best fitting model.

If the value of remove.AR is too low the spectrum could become distorted, so use with care. Note, however, that the value of remove.AR will be restricted to within the range $[1,100]$. If the AR order is much larger than this, it's unclear how prewhiten will perform and whether the AR model is appropriate.

Note that this function does not produce a parametric spectrum estimation; rather, it will return the amplitude response of the best-fitting AR model as spec.ar would. Interpret these results with caution, as an AR response spectrum can be misleading.

Details

A fixed number of tapers is applied across all frequencies using psdcore, and subsequent taper-refinements are based on the spectral derivatives of this spectrum; hence, changes in the number of tapers can affect how many adaptive stages may be needed (though there are no formal convergence criteria to speak of).

The taper series of the returned spectrum is constrained using as.tapers(..., minspan=TRUE).

The default behaviour (remove.AR <= 0<="" code="">) is to remove the standard linear model $[f(x) = \alpha x + \beta]$ from the data; however, the user can model the effect of an autoregressive process by specifiying remove.AR.

See Also

psdcore, prewhiten

Documentation for spec.ar.

Examples

#RDEX#\dontrun{
require(psd)
##
## Pilot spectrum
##
data(magnet)
## simply calculate the pilot spectrum with a few tapers
plot(pilot_spec(xc <-  magnet$clean), log="dB", 
     main="Pilot PSDs for MAGNET and its AR-innovations (red)")
## remove the effect of an AR model works exceptionally
## well for the Project MAGNET data:
plot(pilot_spec(xc, remove.AR=10), log="dB", add=TRUE, col="red")
##
#RDEX#}