There are two popular algorithms of resampling non-multiple sample rates: interpolation and over/down multiple resampling.
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Interpolation is restoring of virtual inter-samples (between «real» samples).
Some resampling algorithms can use interpolation for non multiple resampling.
Like spline function, as example.
Interpolation provide some non-linear distortions (artifacts).
Level of these artifacts depend on interpolation quality.
For resampling popular audio sample rates also used algorithm without interpolation.