BUTTERWORTH FILTER APPROXIMATION
The filter passes all frequencies below Ωc. This is called passband of the filter. Also the filter blocks all the frequencies above Ωc. This is called stopband of the filter. Ωc is called cutoff frequency or critical frequency.
No Practical filters can provide the ideal characteristic. Hence approximation of the ideal characteristic are used. Such approximations are standard and used for filter design.
Such three approximations are regularly used.
a) Butterworth Filter Approximation
b) Chebyshev Filter Approximation
c) Elliptic Filter Approximation
Butterworth filters are defined by the property that the magnitude response is maximally flat in the passband.
This equation gives the pole position of H(s) and H(-s).