11. Choice of Interpolation Resolution

GUIDE: Digital Audio Resampling - Julius O. Smith III. Choice of Interpolation Resolution

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Choice of Interpolation Resolution

We now consider the error due to finite precision in the linear interpolation between stored filter coefficients. We will find that the number of bits ${n_\ in the interpolation factor should be about half the filter coefficient word-length ${n_c}$.

Quantized Interpolation Error Bound.

The quantized interpolation factor and its complement are representable as

$\ $\ $\ (10)
$\ $\ $\ (11)

where, since $\ are unsigned, $\. The interpolated coefficient look-up then gives

$\ $\ $\ (12)
  $\ $\ (13)

where second-order errors $\ and $\ are dropped. Since $\, we obtain the error bound


The three terms in Eq. (2.6.2) are caused by coefficient quantization, interpolation quantization, and linear-approximation error, respectively.

Ideal Lowpass Filter.

For the ideal lowpass, the error bound is


Let ${n_l}=1+{n_c}/2$ and require that the added error is at most ${1\. Then we arrive at the requirement

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