Design of notch and multi-notch FIR filters using fractional derivative constraints

In this paper, the design of 1-dimensional (1-D) finite impulse response (FIR) notch filters is achieved constraint to fractional order derivatives. In order to actualize the ideal frequency response, fractional derivative constraints are imposed such that there is no deviation in fractional derivative of designed frequency response at prescribed frequency points. The divergence in designed frequency response and ideal frequency response is curtailed using conventional least square design method along with Lagrange multiplier to attain closed loop filter coefficients. The design of 1-D notch filter and 1-D multi-notch filter is greatly refined subjected to fractional derivative constraints. Finally, the accuracy of proposed method is demonstrated by two design examples.