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Ideal Lowpass Filter

For the ideal lowpass, the error bound is

\begin{displaymath}
\left\vert e_{qq}(t)\right\vert \leq 2^{-n_c} + a 2^{-(n_l+{n_\eta }+1)} + {\pi^2\over 8} 2^{-n_l}.
\end{displaymath}

Let nl=1+nc/2 and require that the added error is at most ${1\over2}2^{-n_c}$. Then we arrive at the requirement

\begin{displaymath}
{n_\eta }\geq {n_c\over2}.
\end{displaymath}


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``The Digital Audio Resampling Home Page'', by Julius O. Smith III.
Copyright © 2014-01-10 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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