lightkurve.periodogram.
LombScarglePeriodogram
(*args, **kwargs)¶Bases: lightkurve.periodogram.Periodogram
Subclass of Periodogram
representing a power spectrum generated using the Lomb Scargle method.
Attributes Summary
Returns the frequency corresponding to the highest peak in the periodogram. 

Returns the power of the highest peak in the periodogram. 

Returns the array of periods, i.e. 

Returns the period corresponding to the highest peak in the periodogram. 
Methods Summary

Bins the power spectrum. 

Returns a copy of the Periodogram object. 

Estimates the SignalToNoise (SNR) spectrum by dividing out an estimate of the noise background. 

Creates a Periodogram from a LightCurve using the LombScargle method. 

Obtain the flux model for a given frequency and time 

Plots the Periodogram. 

Prints a summary of the noncallable attributes of the Periodogram object. 

Smooths the power spectrum using the ‘boxkernel’ or ‘logmedian’ method. 

Returns a 

Exports the Periodogram as an Astropy Table. 
Attributes Documentation
frequency_at_max_power
¶Returns the frequency corresponding to the highest peak in the periodogram.
max_power
¶Returns the power of the highest peak in the periodogram.
period
¶Returns the array of periods, i.e. 1/frequency.
period_at_max_power
¶Returns the period corresponding to the highest peak in the periodogram.
Methods Documentation
bin
(self, binsize=10, method='mean')¶Bins the power spectrum.
The factor by which to bin the power spectrum, in the sense that the power spectrum will be smoothed by taking the mean in bins of size N / binsize, where N is the length of the original frequency array. Defaults to 10.
Method to use for binning. Default is ‘mean’.
Periodogram
objectReturns a new Periodogram
object which has been binned.
copy
(self)¶Returns a copy of the Periodogram object.
This method uses the copy.deepcopy
function to ensure that all
objects stored within the Periodogram are copied.
A new Periodogram
object which is a copy of the original.
flatten
(self, method='logmedian', filter_width=0.01, return_trend=False)¶Estimates the SignalToNoise (SNR) spectrum by dividing out an estimate of the noise background.
This method divides the power spectrum by a background estimated
using a moving filter in log10 space by default. For details on the
method
and filter_width
parameters, see Periodogram.smooth()
Dividing the power through by the noise background produces a spectrum
with no units of power. Since the signal is divided through by a measure
of the noise, we refer to this as a SignalToNoise
spectrum.
Background estimation method passed on to Periodogram.smooth()
.
Defaults to ‘logmedian’.
If method
= ‘boxkernel’, this is the width of the smoothing filter
in units of frequency.
If method = logmedian
, this is the width of the smoothing filter
in log10(frequency) space.
If True, then the background estimate, alongside the SNR spectrum, will be returned.
Periodogram
objectReturns a periodogram object where the power is an estimate of the signaltonoise of the spectrum, creating by dividing the powers with a simple estimate of the noise background using a smoothing filter.
Periodogram
objectThe estimated power spectrum of the background noise. This is only
returned if return_trend = True
.
from_lightcurve
(lc, minimum_frequency=None, maximum_frequency=None, minimum_period=None, maximum_period=None, frequency=None, period=None, nterms=1, nyquist_factor=1, oversample_factor=None, freq_unit=None, normalization='amplitude', ls_method='fast', **kwargs)¶Creates a Periodogram from a LightCurve using the LombScargle method.
By default, the periodogram will be created for a regular grid of frequencies from one frequency separation to the Nyquist frequency, where the frequency separation is determined as 1 / the time baseline.
The min frequency and/or max frequency (or max period and/or min period)
can be passed to set custom limits for the frequency grid. Alternatively,
the user can provide a custom regular grid using the frequency
parameter or a custom regular grid of periods using the period
parameter.
The sampling of the spectrum can be changed using the
oversample_factor
parameter. An oversampled spectrum
(oversample_factor > 1) is useful for displaying the full details
of the spectrum, allowing the frequencies and amplitudes to be
measured directly from the plot itself, with no fitting required.
This is recommended for most applications, with a value of 5 or
10. On the other hand, an oversample_factor of 1 means the spectrum
is critically sampled, where every point in the spectrum is
independent of the others. This may be used when Lorentzians are to
be fitted to modes in the power spectrum, in cases where the mode
lifetimes are shorter than the timebase of the data (which is
sometimes the case for solarlike oscillations). An
oversample_factor of 1 is suitable for these stars because the
modes are usually fully resolved. That is, the power from each mode
is spread over a range of frequencies due to damping. Hence, any
small error from measuring mode frequencies by taking the maximum
of the peak is negligible compared with the intrinsic linewidth of
the modes.
The normalization
parameter will normalize the spectrum to either
power spectral density (“psd”) or amplitude (“amplitude”). Users
doing asteroseismology on classical pulsators (e.g. delta Scutis)
typically prefer normalization="amplitude"
because “amplitude”
has higher dynamic range (high and low peaks visible
simultaneously), and we often want to read off amplitudes from the
plot. If normalization="amplitude"
, the default value for
oversample_factor
is set to 5 and freq_unit
is 1/day.
Alternatively, users doing asteroseismology on solarlike
oscillators tend to prefer normalization="psd"
because power
density has a scaled axis that depends on the length of the
observing time, and is used when we are interested in noise levels
(e.g. granulation) and are looking at damped oscillations. If
normalization="psd"
, the default value for oversample_factor
is
set to 1 and freq_unit
is set to microHz. Default values of
freq_unit
and oversample_factor
can be overridden. See Appendix
A of Kjeldsen & Bedding, 1995 for a full discussion of
normalization and measurement of oscillation amplitudes
(http://adsabs.harvard.edu/abs/1995A%26A…293…87K).
The parameter nterms controls how many Fourier terms are used in the model. Setting the Nyquist_factor to be greater than 1 will sample the space beyond the Nyquist frequency, which may introduce aliasing.
The freq_unit
parameter allows a request for alternative units in frequency
space. By default frequency is in (1/day) and power in (amplitude).
Asteroseismologists for example may want frequency in (microHz)
in which case they would pass freq_unit=u.microhertz
.
By default this method uses the LombScargle ‘fast’ method, which assumes a regular grid. If a regular grid of periods (i.e. an irregular grid of frequencies) it will use the ‘slow’ method. If nterms > 1 is passed, it will use the ‘fastchi2’ method for regular grids, and ‘chi2’ for irregular grids.
Caution: this method assumes that the LightCurve’s time (lc.time) is given in units of days.
The LightCurve from which to compute the Periodogram.
If specified, use this minimum frequency rather than one over the time baseline.
If specified, use this maximum frequency rather than nyquist_factor times the nyquist frequency.
If specified, use 1./minium_period as the maximum frequency rather than nyquist_factor times the nyquist frequency.
If specified, use 1./maximum_period as the minimum frequency rather than one over the time baseline.
The grid of frequencies to use. If given a unit, it is converted to units of freq_unit. If not, it is assumed to be in units of freq_unit. This over rides any set frequency limits.
The grid of periods to use (as 1/period). If given a unit, it is converted to units of freq_unit. If not, it is assumed to be in units of 1/freq_unit. This overrides any set period limits.
Default 1. Number of terms to use in the Fourier fit.
Default 1. The multiple of the average Nyquist frequency. Is overriden by maximum_frequency (or minimum period).
Default: None. The frequency spacing, determined by the time baseline of the lightcurve, is divided by this factor, oversampling the frequency space. This parameter is identical to the samples_per_peak parameter in astropy.LombScargle(). If normalization=’amplitude’, oversample_factor will be set to 5. If normalization=’psd’, it will be 1. These defaults can be overridden.
astropy.units.core.CompositeUnit
Default: None. The desired frequency units for the Lomb Scargle periodogram. This implies that 1/freq_unit is the units for period. With default normalization (‘amplitude’), the freq_unit is set to 1/day, which can be overridden. ‘psd’ normalization will set freq_unit to microhertz.
Default: 'amplitude'
. The desired normalization of the spectrum.
Can be either power spectral density ('psd'
) or amplitude
('amplitude'
).
Default: 'fast'
. Passed to the method
keyword of
astropy.stats.LombScargle()
.
Keyword arguments passed to astropy.stats.LombScargle()
Periodogram
objectReturns a Periodogram object extracted from the lightcurve.
model
(self, time, frequency=None)¶Obtain the flux model for a given frequency and time
Time points to evaluate model.
max power.
Model object with the time and flux model
plot
(self, scale='linear', ax=None, xlabel=None, ylabel=None, title='', style='lightkurve', view=None, unit=None, **kwargs)¶Plots the Periodogram.
Set x,y axis to be “linear” or “log”. Default is linear.
Axes
A matplotlib axes object to plot into. If no axes is provided, a new one will be generated.
Plot x axis label
Plot y axis label
Plot set_title
Path or URL to a matplotlib style file, or name of one of matplotlib’s builtin stylesheets (e.g. ‘ggplot’). Lightkurve’s custom stylesheet is used by default.
{‘frequency’, ‘period’}. Default ‘frequency’. If ‘frequency’, xaxis units will be frequency. If ‘period’, the xaxis units will be period and ‘log’ scale.
Dictionary of arguments to be passed to matplotlib.pyplot.plot
.
Axes
The matplotlib axes object.
show_properties
(self)¶Prints a summary of the noncallable attributes of the Periodogram object.
Prints in order of type (ints, strings, lists, arrays and others). Prints in alphabetical order.
smooth
(self, method='boxkernel', filter_width=0.1)¶Smooths the power spectrum using the ‘boxkernel’ or ‘logmedian’ method.
If method
is set to ‘boxkernel’, this method will smooth the power
spectrum by convolving with a numpy Box1DKernel with a width of
filter_width
, where filter width
is in units of frequency.
This is best for filtering out noise while maintaining seismic mode
peaks. This method requires the Periodogram to have an evenly spaced
grid of frequencies. A ValueError
exception will be raised if this is
not the case.
If method
is set to ‘logmedian’, it smooths the power spectrum using
a moving median which moves across the power spectrum in a steps of
log10(x0) + 0.5 * filter_width
where filter width
is in log10(frequency) space. This is best for
estimating the noise background, as it filters over the seismic peaks.
Periodograms that are unsmoothed have multiplicative noise that is distributed as chi squared 2 degrees of freedom. This noise distribution has a well defined mean and median but the two are not equivalent. The mean of a chi squared 2 dof distribution is 2, but the median is 2(8/9)**3. (see https://en.wikipedia.org/wiki/Chisquared_distribution) In order to maintain consistency between ‘boxkernel’ and ‘logmedian’ a correction factor of (8/9)**3 is applied to (i.e., the median is divided by the factor) to the median values.
In addition to consistency with the ‘boxkernel’ method, the correction of the median values is useful when applying the periodogram flatten method. The flatten method divides the periodgram by the smoothed periodogram using the ‘logmedian’ method. By appyling the correction factor we follow asteroseismic convention that the signaltonoise power has a mean value of unity. (note the signaltonoise power is really the signal plus noise divided by the noise and hence should be unity in the absence of any signal)
The smoothing method to use. Defaults to ‘boxkernel’.
If method
= ‘boxkernel’, this is the width of the smoothing filter
in units of frequency.
If method = logmedian
, this is the width of the smoothing filter
in log10(frequency) space.
Periodogram
objectReturns a new Periodogram
object in which the power spectrum
has been smoothed.
to_seismology
(self, **kwargs)¶Returns a Seismology
object to analyze the periodogram.
Seismology
Helper object to run asteroseismology methods.