# Fractional Delay Filters and Cutoff Frequences

I am trying to implement an interpolator for arbitrary sampling rate conversion of a one-dimensional signal (a fractional delay filter). I am aware of the fact that interpolation is in general a problem of low-pass filtering, and impulse response and passband widths are inversely proportionate (for the same kernel shape). However, I'm a bit uncertain of how precisely to apply this to fractional delay filters for different interpolation rates.

As I understand it, the frequency cutoff for the interpolation kernel should be at pi*low_rate/high_rate radians. But for what class of interpolation filters is this the case? E.g. for cubic B-spline interpolation (a non-Nyquist(1) piecewise polynomial, where Nyquist(1) means the filter's impulse response is delta when the source and target sampling rates are identical) for supersampling the kernel is based purely on the fractional position, and does not have any kind of provision for a cutoff, despite it being possible to compute an impulse response for the interpolator (which would seem to make the kernel frequency-dependent by the impulse response/passband duality mentioned previously). What about for other classes of interpolators such as linear (Nyquist(1), polynomial), sinc (Nyquist(1), non-polynomial) or Gaussian (non-Nyquist(1), non-polynomial)?

Additionally, non-Nyquist(1) interpolators can by converted to Nyquist(1) with the use of a fixed prefilter, e.g. as described in Variable Sample Rate Conversion Techniques for the Advanced Receiver. If in fact a given interpolator must have its impulse response dilated/contracted based on cutoff frequency, this means there are now two stages for these non-Nyquist(1) interpolators: the fixed prefilter and the potentially variable interpolation. At what stage(s) would the correction for cutoff frequency be applied in such a system, and would it follow the same formula stated above? I would have expected frequency correction to be necessary in the prefilter, but the paper doesn't seem to indicate the use of frequency-dependent prefilters with cubic B-spline interpolation despite that interpolator, as already stated, having no accommodation for cutoff frequency in the core algorithm.