Ok, I must be confused about resampling. Here's a demo of a resampler I just wrote, which should be able to perfectly resample any periodic signal in O(n log n) time, where n is max(old period, new period). The idea is to use Bluestein FFT and drop the negative frequencies. It works instantly for e.g. resampling from 10007 to 10009 samples per period and then back, where your method would require going to 100160063. The round trip precision is 1e-15, and the graphs look reasonable. And at least from the theory I can figure out, it should never add new information, never alias, and should remove information only when downsampling. What am I missing?