Bandwidth of One Pole

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

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

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

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

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.