psd-normalization: Normalization of power spectral density estimates.

In abarbour/psd: Adaptive, Sine-Multitaper Power Spectral Density and Cross Spectrum Estimation

Normalization of power spectral density estimates.

Description

Normalize power spectral densities from various estimators into single-sided spectra.

Usage

normalize(Spec, ...)

## S3 method for class 'list'
normalize(Spec, ...)

## S3 method for class 'spec'
normalize(
  Spec,
  Fsamp = 1,
  src = c("spectrum", "double.sided", "psd", "single.sided"),
  verbose = TRUE,
  ...
)

## S3 method for class 'amt'
normalize(Spec, ...)

Arguments

Spec	spectrum to normalize
...	(unused) additional parameters
Fsamp	sampling frequency
src	character string; the source of the spectrum estimator
verbose	logical; should messages be given?

Details

Normalizations commonly encountered for power spectra depend on it's assumed sidedness: whether the spectrum is either single- or double-sided. The normalizations performed here enforce single-sidedness, and correct as necessary.

Frequencies are assumed to be based on the Nyquist frequency (half the sampling rate). For example: If a series X has sampling frequency F_S, then the PSD frequencies will span [0,F_S/2].

For amplitudes, improper normalization can can introduce errant factors of either 1/2 or F_S into the estimates, depending on the assumed sidedness. These factors can be accounted for with the src argument, which defaults to normalizing a double-sided spectrum.

Value

An object with its spectral values normalized accordingly.

Spectrum sidedness and the src argument

"double.sided" or "spectrum"

These spectra assume frequency range of [-F_S/2,F_S/2], and so are normalized by scaling by a factor of two upwards. Some estimators producing double-sided spectra:

• stats::spectrum

• RSEIS::mtapspec

"single.sided" or "psd"

As mentioned before, these spectra assume frequency range of [0,F_S/2] and are scaled only by the inverse of the sampling rate. Some estimators producing single-sided spectra:

• psdcore

Author(s)

A.J. Barbour

See Also

psdcore, spectral_properties

Examples

## Not run: #REX
library(psd)

##
## Normalization
##

# timeseries with sampling frequency **not** equal to 1:
set.seed(1234)
X <- ts(rnorm(1e3), frequency=20)

# spec.pgram: double sided
pgram <- spectrum(X)

# psdcore: single sided
PSD <- psdcore(X)

# note the normalization differences:
plot(pgram, log="dB", ylim=c(-40,10))
plot(PSD, add=TRUE, col="red", log="dB")

# A crude representation of integrated spectrum: 
#   should equal variance of white noise series (~= 1)
mean(pgram[['spec']]) * max(pgram[['freq']])
mean(PSD[['spec']]) * max(PSD[['freq']])

# normalize 
pgram <- normalize(pgram, src="spectrum")
PSD <- normalize(pgram, src="psd")
# replot them
plot(pgram, log="dB", ylim=c(-40,10))
plot(PSD, add=TRUE, col="red", log="dB")

# Again, integrated spectrum should be ~= 1:
mean(pgram[['spec']]) * max(pgram[['freq']])
mean(PSD[['spec']]) * max(PSD[['freq']])



## End(Not run)#REX

abarbour/psd documentation built on Aug. 15, 2023, 8:56 a.m.