A How can I resample data with errors linearly in log space?

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I need to resample a set of data and its errors linearly in log space, with the same number of points. I was just going to interpolate between points to get the data - but how do I calculate the errors?
 
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what do you mean with "resample" if then you talk about interpolating them?
 
If you're interpolating data points, why not interpolate their errors? The errors produce two additional sets of data points above/below the original data. Treat them the same way you're treating your original data.

I assume the "data" are from a numerical simulation? Otherwise it is probably not legit to interpolate experimental errors.
 
Its experimental errors in astronomy in a spectra. It seems to be quite a commonly done thing - rebinning from linear wavelength to logarithmic whilst maintaining the overall signal to noise. Given that it is "non legit" I should have probably asked in the physics rather than maths forum!

For example I have done it using this IRAF package. http://drforum.gemini.edu/wp-content/uploads/2014/05/README.txt
 

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