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

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

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