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The filter passes all frequencies below Ωc. This is called passband of the filter.

**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).

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