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Choice of Table Size and Word Lengths

It is desirable that the stored filter impulse response be sampled sufficiently densely so that interpolating linearly between samples does not introduce error greater than the quantization error. It is shown in [464] that this condition is satisfied when the filter impulse-response table contains at least $ L=2^{1+n_c/2}$ entries per ``zero-crossing'', where $ n_c$ is the number of bits allocated to each table entry. (A later, sharper, error bound gives that $ L=2^{n_c/2}$ is sufficient.) It is additionally shown in [464] that the number of bits in the interpolation between impulse-response samples should be near $ n_c/2$ or more. With these choices, the linear interpolation error and the error due to quantized interpolation factors are each about equal to the coefficient quantization error. A signal resampler designed according to these rules will typically be limited primarily by the lowpass filter design, rather than by quantization effects.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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