With regards to the answer in this post Is it possible to do deconvolution with two data sets that have different sampling rates?
I suggest the possibility of compensating for a residual resampling error with a quadratic phase versus frequency function. I haven't seen this done and have not confirmed its effectiveness or the limits of its use. My question is if anyone has done this or seen it used (as if possible I would imagine it to be commonly used), or if there is clarity on why such an approach would be flawed.
The considered approach would be to remove residual frequency sampling error with use of a all-pass function that has a quadratic phase versus frequency response. (A linear phase versus frequency is a fixed time delay, so a quadratic phase versus frequency would have a time delay that linearly increases versus frequency, in such a direction to compensate for the phase error that linearly increases or decreases versus frequency depending on the sign of the error).
I realize that it may not provide a perfect compensation since the result would be a linear delay versus frequency, but am imagining utility to the same extent that we can approximate a phase shift over narrow frequency ranges with a fixed time delay (it is the desired phase shift at one frequency and then deviates linearly from there). In the case of applying this to a fixed length FFT, note that the effect of a shift in the sampling rate will cause each frequency bin to shift by a certain phase (quadratically dependent on the frequency), so the compensation at each frequency bin should be exact.
I feel I may be missing something obvious. Could this approach reduce residual frequency sampling error?