Question about spectral smoothing

[Antares1234]

There are some examples of spectral smoothing in the docs, and I am a little confused about the Gaussian kernels in these examples.

It seems that the FWHM of the Gaussian kernel is calculated in different ways in the two examples. The former is 2/0.5, while the latter is (0.25^2 - 0.1^2)^0.5/0.1. Why doesn't the latter use 0.25/0.1 as the FWHM?

[keflavich]

The Gaussian1DKernel object takes a value in units of pixels.

When you convolve two Gaussians, the result is a Gaussian with width: $$\sigma^2{final} = \sigma^2{1} + \sigma^2_{2}$$

The first above example is smoothing by 4 pixels FWHM, which smooths by 4 pixels. If the original data had resolution of 0.1 km/s, this would result in smoothing to (0.1^2 + (4/2.35 * 0.1)^2)^0.5 = 0.197 km/s. The second example smooths to a target resolution of 0.25 km/s.

[Antares1234]

I see. Thanks for your explanation. And there is another question. I'm reading the cube projection tutorial: https://learn.astropy.org/tutorials/SpectralCubeReprojectExample.html.

Here the standard deviation of the kernel is 1.886/2.35. Why isn't it divided by the original pixel width (velocity_res_2)?

[keflavich]

Good catch, that looks like an error. It would be helpful to propose a suggested fix there!