# 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 x-axis (in any frequency units) and values of power on the y-axis (in units of ppm^2 / [frequency units]).

Attributes: frequency : Array of frequencies with associated astropy unit. power : Array of power-spectral-densities. The Quantity array must have units of ppm^2 / freq_unit, where freq_unit is the unit of the frequency attribute. nyquist : float, optional The Nyquist frequency of the lightcurve. In units of freq_unit, where freq_unit is the unit of the frequency attribute. label : str, optional Human-friendly object label, e.g. “KIC 123456789”. targetid : str, optional Identifier of the target. default_view : “frequency” or “period” Should plots be shown in frequency space or period space by default? meta : dict, optional Free-form metadata associated with the Periodogram.

Attributes Summary

 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. period_at_max_power Returns the period corresponding to the highest peak in the periodogram.

Methods Summary

 bin([binsize, method]) Bins the power spectrum. copy() Returns a copy of the Periodogram object. flatten([method, filter_width, return_trend]) Estimates the Signal-To-Noise (SNR) spectrum by dividing out an estimate of the noise background. Periodogram.from_lightcurve plot([scale, ax, xlabel, ylabel, title, …]) Plots the Periodogram. show_properties() Prints a summary of the non-callable attributes of the Periodogram object. smooth([method, filter_width]) Smooths the power spectrum using the ‘boxkernel’ or ‘logmedian’ method. to_table() 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(binsize=10, method='mean')

Bins the power spectrum.

Parameters: binsize : int 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 : str, one of ‘mean’ or ‘median’ Method to use for binning. Default is ‘mean’. binned_periodogram : a Periodogram object Returns a new Periodogram object which has been binned.
copy()

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_copy : Periodogram A new Periodogram object which is a copy of the original.
flatten(method='logmedian', filter_width=0.01, return_trend=False)

Estimates the Signal-To-Noise (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 Signal-To-Noise spectrum.

Parameters: method : str, one of ‘boxkernel’ or ‘logmedian’ Background estimation method passed on to Periodogram.smooth(). Defaults to ‘logmedian’. filter_width : float 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_trend : bool If True, then the background estimate, alongside the SNR spectrum, will be returned. snr_spectrum : Periodogram object Returns a periodogram object where the power is an estimate of the signal-to-noise 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.
plot(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 : matplotlib.axes._subplots.AxesSubplot A matplotlib axes object to plot into. If no axes is provided, a new one will be generated. xlabel : str Plot x axis label ylabel : str Plot y axis label title : str Plot set_title style : str Path or URL to a matplotlib style file, or name of one of matplotlib’s built-in stylesheets (e.g. ‘ggplot’). Lightkurve’s custom stylesheet is used by default. view : str {‘frequency’, ‘period’}. Default ‘frequency’. If ‘frequency’, x-axis units will be frequency. If ‘period’, the x-axis units will be period and ‘log’ scale. kwargs : dict Dictionary of arguments to be passed to matplotlib.pyplot.plot. ax : matplotlib.axes._subplots.AxesSubplot The matplotlib axes object.
show_properties()

Prints a summary of the non-callable attributes of the Periodogram object.

Prints in order of type (ints, strings, lists, arrays and others). Prints in alphabetical order.

smooth(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/Chi-squared_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 signal-to-noise power has a mean value of unity. (note the signal-to-noise power is really the signal plus noise divided by the noise and hence should be unity in the absence of any signal)

Parameters: method : str, one of ‘boxkernel’ or ‘logmedian’ The smoothing method to use. Defaults to ‘boxkernel’. filter_width : float 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. smoothed_pg : Periodogram object Returns a new Periodogram object in which the power spectrum has been smoothed.
to_table()

Exports the Periodogram as an Astropy Table.

Returns: table : An AstroPy Table with columns ‘frequency’, ‘period’, and ‘power’.

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