Finally from eqs. and , the resampled channel weight is4:
This relation has a non-intuitive effect on the resampled spectrum: its weight is, in the general case, different from the original one. Let's assume that the spectrum is resampled onto a spectrum with the same resolution but with a shifted value at reference channel (fig. ). In such a case, the channel weight we can deduce, and its associated , are:
This should be kept in mind when averaging e.g. two and spectra with same resolution but shifted X-axis. If a SIGMA weighting is invoked, the average won't be found at the mean distance of the two spectra even if their are equal!
One should also take care that eq. assumes
uncorrelated input channels. Resampling a spectrum which
was already resampled (e.g.
a correlation between more contiguous channels. In particular
this equation should not be used to compute the associated
The weight at eq. apply to the TIME and SIGMA weighting, where the computations above have a physical meaning and one can expect consistant values for integration time, channel width and . For the EQUAL weighting, user expects the two input spectra to have the same weight whatever their abscissa axis definition: this means that a re-EQUALization of the channels must come after the resampling. The ad hoc weighting is in this case: