issue_comments: 805783942

Would it be conceivable to implement an alternative form of coordinate index which is explicitly a linear coordinate axis, storing only a first point and a step (possibly a last point but that would obviously be redundant with the length of the dimension). This would be trivial to pad via linear extrapolation and the pad function would just have to ask the coordinate to pad itself. This could also in principle extend to other coordinates like a periodic one etc., although I don't personally have a use for those. Coordinates that don't know how to handle being padded can use NaN as currently. I guess that this is one of the things that could be enabled by #1603?

My use case is in MRI reconstruction where we frequently have asymmetric datasets and need to pad them to be symmetric before an IFT. I am using xrft which is great but makes a fuss if the coordinates are not correctly linear and centred on the origin. The degree of asymmetry and the step size change from dataset to dataset, so it is not trivial to assemble the necessary new coordinate values for @fujiisoup's proposed solution.