Horse power most certainly can make difference in more accurate
interpolation. The more points (higher order) the more accurate the
interpolation. The more points the more computing power needed to do it
within the same amount of time.

Couple snippets from Google Searches: Is the whole world wrong that
interpolation doesn't work !!

The EMU10K1 uses E-mu's patented 8-point interpolation engine for
higher quality audio samples or SoundFont(R) banks. Interpolation
increases the number of samples which can more accurately reconstruct
the original sound.

DSP Strategies for Faster Polynomial Interpllation 
An algorithm for calculating a real-time sampling-rate conversion via
low-order polynomial interpolation of a digital signal is described.
Modifications to common DSP chip architectures are then suggested which
will reduce the computational complexity of the presented algorithm
compared to that of the classical algorithm.


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