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Bandwidth of One Pole

A typical formula relating 3-dB bandwidth $ B$ (in Hz) to the pole radius $ R\in[0,1)$ is

$\displaystyle \zbox {R = e^{- \pi B T}} \protect$ (9.7)

where $ T$ denotes the sampling interval as usual. Solving for $ B$ gives

$\displaystyle B = - \frac{\ln(R)}{\pi T}.
$

In §E.6 (see also §B.1.3), it is shown that $ B$ is the 3-dB bandwidth or half-power bandwidth, in the limit, as the sampling rate goes to infinity.


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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