Seconding this. It’s good to know what mathematical methods to use, but you definitely don’t need to because the problem of resampling has been solved 100 times for you in various libraries. Use libspeexdsp (included in Rack and wrapped with dsp/resampler.hpp) if you have a fixed resampling ratio or libsamplerate if the ratio is variable over time, or Rubberband or SoundTouch if you need pitch/time stretching.
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