The psd module

apollinaire.psd.series_to_psd(series, dt, correct_dc=True)

Take a timeseries and compute its PSD

Parameters:

• series (ndarray) – input timeseries.

• dt (float) – sampling of the timeseries, in seconds.

• correct_dc (bool) – if set to True, will compute the duty_cycle to adjust the psd values. Optional, default False.

Returns:

frequency and psd array. The frequency units are in Hz and the PSD in series_units**2/Hz. Note that the apollinaire.peakbagging submodule works with frequency in muHz and PSD in ppm**2/muH (or (m/s)**2/muHz for radial velocity PSD), frequency array and PSD should therefore be normalised accordingly before using the peakbagging functions.

Return type:

tuple of ndarray

apollinaire.psd.echelle_diagram(freq, PSD, dnu, twice=False, fig=None, index=111, figsize=(16, 16), title=None, smooth=10, cmap='cividis', cmap_scale='linear', mode_freq=None, mode_freq_err=None, vmin=None, vmax=None, scatter_color='white', fmt='+', ylim=None, shading='gouraud', mfc='none', ms=20, index_offset=None, mec=None, xlabel=None, ylabel=None, **kwargs)

Build the echelle diagram of a given PSD.

Parameters:

• freq (ndarray) – input vector of frequencies.

• PSD (ndarray) – input vector of power. Must be of same size than freq.

• dnu (float) – the large frequency separation use to cut slices into the diagram.

• twice (bool) – slice using 2 x dnu instead of dnu, default False.

• fig (matplotlib Figure) – figure on which the echelle diagram will be plotted. If None, a new figure instance will be created. Optional, default None.

• index (int) – position of the echelle diagram Axe in the figure. Optional, default 111.

• figsize (tuple) – size of the echelle diagram to plot.

• title (str) – title of the figure. Optional, default (16, 16)

• smooth (int) – size of the rolling window used to smooth the PSD. Default 10.

• cmap (str) – select one available color map provided by matplotlib, default cividis

• cmap_scale (str) – scale use for the colormap. Can be ‘linear’ or ‘logarithmic’. Optional, default ‘linear’.

• mode_freq (ndarray or tuple of array) – frequency array of the modes to represent on the diagram. It can be single array or a tuple of array.

• mode_freq_err (ndarray or tuple of array) – frequency uncertainty of the modes to represent on the diagram. It can be a single array or a tuple of array.

• vmin (float) – minimum value for the colormap.

• vmax (float) – maximum value for the colormap.

• scatter_color (str) – color of the scatter point of the mode frequencies. Optional, default white.

• fmt (str or tuple) – the format of the errorbar to plot. Can be a single string or a tuple of string with the same dimension that mode_freq.

• ylim (tuple) – the y-bounds of the echelle diagram.

• mew (float) – marker edge width. Optional, default 1.

• markersize (float) – size of the markers used for the errorbar plot. Optional, default 10.

• capsize (float) – length of the error bar caps. Optional, default 2.

Returns:

the matplotlib Figure with the echelle diagram.

Return type:

matplotlib Figure

apollinaire.psd.tf(series, dt)

Take a timeseries and compute its properly normalised Fourier transform.

Parameters:

• series (ndarray) – input timeseries

• dt (float) – sampling of the timeseries

Returns:

frequency and psd array

Return type:

tuple of ndarray

apollinaire.psd.tf_to_psd(tf, T)

Parameters:

• tf (ndarray) – complex Fourier transform from which to compute the PSD.

• T (float) – resolution of the Fourier transform.

Returns:

corresponding PSD

Return type:

ndarray

apollinaire.psd.plot_psd_fits(filename, rv=True, index=0)

Plot the PSD of a fits file containing frequency and power array. The frequency in the file are supposed to be in Hz and the power in (m/s)^2/Hz (spectroscopy) or ppm^2/Hz (photometry)

Parameters:

• filename (str) – name of the fits file

• rv (bool) – set to True if it is a radial velocity PSD, to False if it is a photometric PSD.

• index (int) – index of the hdulist of the fits file where the PSD can be found. Default is 0.