periodogram.Rd
This function calculates isotropic LombScargle periodogram (LSP, Scargle, 1982) from a telemetry object. One of two algorithms is used. The slow \(O(n^2)\) algorithm vectorizes the exact relations of Scargle (1982), while the fast \(O(n \log n)\) algorithm uses the FFT method described in Péron & Fleming et al (2016). The latter method is exact if the data are evenly scheduled, permitting gaps, and otherwise it can be made arbitrarily precise via the res.time
option.
periodogram(data,CTMM=NULL,dt=NULL,res.freq=1,res.time=1,fast=NULL,axes=c("x","y")) # S3 method for periodogram plot(x,max=FALSE,diagnostic=FALSE,col="black",transparency=0.25,grid=TRUE,...)
data 


CTMM  An optional 
dt  Sampling interval for frequency cutoff. 
res.freq  Multiplier to inflate the frequency resolution. 
res.time  Integer multiplier to inflate the temporal resolution. Useful when 
fast  Use the exact algorithm if FALSE, the FFT algorithm if TRUE, and further inflate the frequency resolution to a power of two sample size if 
axes  Array of axes to calculate an average (isotropic) variogram for. 
x  Output object of 
max  Plot only the local maxima of the periodogram. Use only with 
diagnostic  Plot the sampling schedule's periodogram to check for spurious periodicities. 
col  Color of periodogram. 
transparency  Adds transparency to clustered data if greater than zero. Should be less than one. 
grid  Whether or not to plot gridlines at common periodicities. 
...  Optional arguments fed to 
If no dt
is specified, the median sampling interval is used. This is typically a good assumption for most data, even when there are gaps and this choice corresponds to the discrete Fourier transform (DFT) periodogram for evenlysampled data.
At default resolution the frequency grid interval is given by 1/(2*(range(data$t)+dt))
and the frequency cutoff is given by 1/(2*dt)
, both in accordance with the DFT periodogram. Increasing res.freq
beyond res.freq=1
will make for a smooth periodogram, but sequential frequencies will be highly correlated. The max=TRUE
option to plot.periodogram
may be useful for res.freq>1
. Increasing res.time
beyond res.time=1
is helpful if there is variability in the sampling rate and fast>0
.
If a CTMM
argument is provided, the ML mean will be detrended from the data prior to calculating the periodogram. Otherwise, the sample mean will be detrended.
If a list of telemetry
objects are fed into periodogram
, then a mean periodogram
object will be returned with the default dt
and base frequency resolution selected on a worst case basis according to the method described by Péron & Fleming et al (2016).
Returns a periodogram object (class periodogram
) which is a dataframe containing the frequency, f
and the LombScargle periodogram at that frequency, LSP
.
J. D. Scargle, ``Studies in astronomical timeseries analysis. II. Statistical aspects of spectral analysis of unevenlysampled data'', The Astrophysical Journal, 263, 835853 (1952) doi: 10.1086/160554 .
G. Péron, C. H. Fleming, R. C. de Paula, J. M. Calabrese, ``Uncovering periodic patterns of space use in animal tracking data with periodograms, including a new algorithm for the LombScargle periodogram and improved randomization tests'', Movement Ecology, 4:19 (2016) doi: 10.1186/s4046201600847 .
C. H. Fleming and G. Péron
The LSP is totally inappropriate if you in any way alter the sampling rate within the dataset. Stick with variograms in that case. There is a diagnostic
option in plot.periodogram
that can check for spurious periodicities that result from an autocorrelated sampling schedule. This plot will not contain any periodicities if the LSP is appropriate.
res.time>1
relies on Lagrange interpolation of the sinusoids (not the data), which can suffer from Runge's phenomena. periodogram
tests for an invalid result and can fail with an error message. For whatever reason, this more frequently seems to happen when res.time=3
.
#Load package and data library(ctmm) data(wolf) #Extract movement data for a single animal Tay < wolf$Tay #Calculate periodogram (fast==2 for a speedy example) #There is some variability in the sampling frequency, so we increase res.time LSP < periodogram(Tay,fast=2,res.time=2) #Plot the periodogram plot(LSP,max=TRUE)