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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