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  that this condition is satisfied when the filter impulse-response table contains at least entries per ``zero-crossing'', where is the number of bits allocated to each table entry. (A later, sharper, error bound gives that is sufficient.) It is additionally shown in  that the number of bits in the interpolation between impulse-response samples should be near 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.
Differentiator Filter Bank