Matt Daunt (NYU) and I had lunch today and discussed various things. One is the idea that we need (for technical reasons of data analysis) to make and use continuous representations of spectra. That is, we need to represent our spectra of stars such that they can be exactly and losslessly interpolated to any (sufficiently fine) grid of points. The ESA Gaia Mission XP spectra have this property: They are represented as polynomial basis functions, which confuse and surprise everyone. They are hard! But there are many other choices. For example, if the spectra are represented with b-spline basis coefficients, the coefficients “look like” just a set of flux values at wavelengths (so traditionalists are happy), but in fact they are the parameters of a continuous model that can be interpolated losslessly to any grid.
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