Bandwidth of One Pole

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

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

(9.7)

where

denotes the sampling interval as usual. Solving for

gives

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

In §E.6 (see also §B.1.3), it is shown that

is the 3-dB bandwidth or half-power bandwidth, in the limit, as the sampling rate goes to infinity.

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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