Novel band-pass and notch filter with dynamic damping of fractional order

The paper introduces a novel the second order band-pass and notch filter with dynamic damping factor β
_d
of fractional order. Indeed, the factor β
_d
has a form of fractional differentiator of order α, i.e. β
_d
=β/s
^α
, where β and α are adjustable parameters. Shaping of the frequency response enables achieving better phase response compared to the integer-order counterparts which is of great concern in many applications. The aim of the paper is to exploit an extra degree of freedoms of presented filters to achieve the desired filter specifications and obtain desired response in the frequency and the time domain.