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In order to subtract the continuum from a spectrum and to get a whitened spectrum, I did the spectral whitening for a test spectrum. The spectral whitening is performed in the following procedure:
- Fourier transformation of a spectrum
- Apply a bandpass filter in the wavenumber domain to extract only the large wavenumber (small-scale) components
- Inverse Fourier transform of the filtered spectrum, which should have been whitened.
I used a simulated spectrum similar to the PFS outputs made from the observed SDSS spectrum of an F-star. I used two high-pass filters, the boxcar and Tukey. The results were check, particularly, at four absorption lines which are strongly depending on the stellar parameters. In any cases with the boxcar filter, the small undulations (sinc functions) are left on the continuum, while those undulations subside around the monitored lines in the case with Tukey filter. It is difficult that both Balmer lines and other narrow lines survive at the same time, because the large widths of Balmer lines are close to the middle-scale fluctuations of the continuum which we want to subtract. I found the resultant spectra of the spectral whitening is very sensitive to a parameter of an adopted filter (e.g., the cut-out wavenumber and the shape parameter). The details are as follows.
Test spectrum
I am using similar spectra to the PFS outputs. To make simulated spectra, I multiplied the observed SDSS spectra of F-stars in Lee et al. (2011) by the atmospheric transmission and then divided it by the flat spectrum (from the quartz lamp).
Parameter dependence of absorption lines
Before doing the spectral whitening, I checked the absorption lines that are strongly depending on the stellar parameters (Teff, log g, Z, and [alpha/Fe]). Because these lines are important in stellar classification, I monitor these lines and the continua by them during the whitening process. Four figures below are the standard deviations (blue) and differences between max and min (red) of each wavelength among a subset of AMBRE templates. The left figure is made among a subset in which three parameters (log, Z, and [alpha/Fe]) are fixed but Teff is free (from 5500 K to 8000 K). Similarly, other figures are free in each parameters (logg, Z, and [alpha/Fe]). Balmer series are sensitive to Teff. Na D/He I and Paschen series are sensitive to Teff, Logg, and Z. Mg I triplets are to Logg, Z, and [alpha/Fe]. Ca II triplets are sensitive to all the parameters.
   
Spectral whitening
I tested two filters of the boxcar filter and Tukey filter (https://scipy.github.io/devdocs/generated/scipy.signal.windows.tukey.html). Each figure shows the input spectrum (top panel), the power spectrum and filtered one (second row from the top), the whitened spectrum from the inverse Fourier transform of the filtered spectrum (third row), and four absorption lines I am monitoring (bottom). Different figures are results with different filters and different parameters of a filter. In the bottom panel, the spectra whose local continua were subtracted using a sigma-clipped median value.
Boxcar filter
In these four cases with the boxcar filter, the different cut-out wavenumber are adopted: 1/log10(wavelength/AA) = 200, 300, 400, 500, which are close values to a wavenumber roughly comparable to or slightly less than the scale of Balmer lines.
   
I also show the case that the cut-out wavenumber of 20 is used to make the Balmer lines survive.
Tukey filter
I tried to delete the small undulations of sinc functions in the boxcar cases and I used a Tukey filter for that. We can control the width and the sharpness of the filter. The undulations subsided around the monitored lines if we choose a proper parameters of the filter. The high sharpness of the filter makes the spectrum flat, but that makes the lines narrow and removes Balmer lines. On the other hand, in the case of the low sharpness, Balmer lines survive but the continuum still remains.
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Alpha_fixedt6000_g4.0_z0.0.png
