Design of maximally flat linear phase FIR notch filter with controlled null width

A technique for designing a maximally flat, linear phase FIR notch filter with controlled null width is presented in this paper. Design analysis is carried out with first-, third- and fifth-order zero derivative constraints of the amplitude response of the FIR filter at notch frequency. An algorithm is presented for designing maximally flat, linear phase FIR notch filter with specified null width around specified notch frequency with third-order zero derivative constraint at the notch frequency. Detailed analysis in this paper shows that the null width of a maximally flat, linear phase FIR notch filter can be controlled by suitable selection of individual zero-odd-order derivatives and also by the successive addition of zero-odd-order derivatives at the notch frequency.