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Table Look-Up

A general approach to variable filtering is to tabulate the filter coefficients as a function of the desired variables. In the case of fractional delay filters, the impulse response $ h_\Delta(n)$ is tabulated as a function of delay $ \Delta = N/2+\eta$, $ \eta\in[-1/2,1/2)$, $ n=0,1,2,\ldots,N$, where $ N$ is the interpolation-filter order. For each $ n$, $ \Delta$ may be sampled sufficiently densely so that linear interpolation will give a sufficiently accurate ``interpolated table look-up'' of $ h_\Delta(n)$ for each $ n$ and (continuous) $ \Delta$. This method is commonly used in closely related problem of sampling-rate conversion [462].

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Polynomials in the Delay
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Order 5 over a range of fractional delays