Periodogram¶

class
lightkurve.periodogram.
Periodogram
(frequency, power, nyquist=None, label=None, targetid=None, default_view='frequency', meta={})¶ Bases:
object
Generic class to represent a power spectrum (frequency vs power data).
The Periodogram class represents a power spectrum, with values of frequency on the xaxis (in any frequency units) and values of power on the yaxis (in units of flux^2 / [frequency units]).
 Attributes
 frequency
Quantity
Array of frequencies as an AstroPy Quantity object.
 power
Quantity
Array of powerspectraldensities. The Quantity must have units of
flux^2 / freq_unit
, where freq_unit is the unit of the frequency attribute. nyquistfloat
The Nyquist frequency of the lightcurve. In units of freq_unit, where freq_unit is the unit of the frequency attribute.
 labelstr
Humanfriendly object label, e.g. “KIC 123456789”.
 targetidstr
Identifier of the target.
 default_view“frequency” or “period”
Should plots be shown in frequency space or period space by default?
 metadict
Freeform metadata associated with the Periodogram.
 frequency
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
bin
(self[, binsize, method])Bins the power spectrum.
copy
(self)Returns a copy of the Periodogram object.
flatten
(self[, method, filter_width, …])Estimates the SignalToNoise (SNR) spectrum by dividing out an estimate of the noise background.
plot
(self[, scale, ax, xlabel, ylabel, …])Plots the Periodogram.
show_properties
(self)Prints a summary of the noncallable attributes of the Periodogram object.
smooth
(self[, method, filter_width])Smooths the power spectrum using the ‘boxkernel’ or ‘logmedian’ method.
to_seismology
(self, \*\*kwargs)Returns a
Seismology
object to analyze the periodogram.to_table
(self)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.
 Parameters
 binsizeint
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.
 methodstr, one of ‘mean’ or ‘median’
Method to use for binning. Default is ‘mean’.
 Returns
 binned_periodograma
Periodogram
object Returns a new
Periodogram
object which has been binned.
 binned_periodograma

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. Returns
 pg_copyPeriodogram
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
andfilter_width
parameters, seePeriodogram.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. Parameters
 methodstr, one of ‘boxkernel’ or ‘logmedian’
Background estimation method passed on to
Periodogram.smooth()
. Defaults to ‘logmedian’. filter_widthfloat
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. return_trendbool
If True, then the background estimate, alongside the SNR spectrum, will be returned.
 Returns
 snr_spectrum
Periodogram
object Returns 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.
 bkg
Periodogram
object The estimated power spectrum of the background noise. This is only returned if
return_trend = True
.
 snr_spectrum

plot
(self, scale='linear', ax=None, xlabel=None, ylabel=None, title='', style='lightkurve', view=None, unit=None, **kwargs)¶ Plots the Periodogram.
 Parameters
 scale: str
Set x,y axis to be “linear” or “log”. Default is linear.
 ax
Axes
A matplotlib axes object to plot into. If no axes is provided, a new one will be generated.
 xlabelstr
Plot x axis label
 ylabelstr
Plot y axis label
 titlestr
Plot set_title
 stylestr
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.
 viewstr
{‘frequency’, ‘period’}. Default ‘frequency’. If ‘frequency’, xaxis units will be frequency. If ‘period’, the xaxis units will be period and ‘log’ scale.
 kwargsdict
Dictionary of arguments to be passed to
matplotlib.pyplot.plot
.
 Returns
 ax
Axes
The matplotlib axes object.
 ax

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 offilter_width
, wherefilter 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. AValueError
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 oflog10(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)
 Parameters
 methodstr, one of ‘boxkernel’ or ‘logmedian’
The smoothing method to use. Defaults to ‘boxkernel’.
 filter_widthfloat
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.
 Returns
 smoothed_pg
Periodogram
object Returns a new
Periodogram
object in which the power spectrum has been smoothed.
 smoothed_pg

to_seismology
(self, **kwargs)¶ Returns a
Seismology
object to analyze the periodogram. Returns
 seismology
Seismology
Helper object to run asteroseismology methods.
 seismology