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I have a spectral cube (in FITS format) whose spectral dimension is in ångströms. The sampling along the spectral dimension is 0.28A (CDELT=0.28). The observation in the cube is Ha emission of a galaxy at redshift 0.1.

How can I convert the sampling to km/s?

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If you want bins that have an equal step in km/s then you will have to rebin in steps of equal log wavelength. On this scale the rest wavelength of H alpha is at zero km/s and then each bin will represent a increment in velocity with respect to that.

See How do I apply a velocity shift to a wavelength array with uniform logarithmic spacing?

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