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 [464].