Resampling an audio signal
There are some excellent papers on this topic you might want to read.

Sampling-50 years after Shannon, M Unser - Proceedings of the IEEE, 2000

Splines: A perfect fit for signal and image processing, M Unser - IEEE Signal processing magazine, 1999

Interpolation and decimation of digital signals—A tutorial review, RE Crochiere, LR Rabiner - Proceedings of the IEEE, 1981.