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Analog Prototype Filter

Since the digital cut-off frequency may be set to any value, irrespective of the analog cut-off frequency, it is convenient to set the analog cut-off frequency to $ \omega_c = 1$ . In this case, the bilinear-transform constant $ c$ is simply set to

$\displaystyle c = \cot(\omega_cT/2)
$

when carrying out mapping Eq.$ \,$ (I.9) to convert the analog prototype to a digital filter with cut-off at frequency $ \omega_c$ .


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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
CCRMA