On the design of multi notch filters

A methodology for designing FIR multi notch filters (NFs) derived from second‐order prototype IIR NFs is suggested. Rejection bandwidth for the designed filter can be controlled by suitable choice of ‘r’, the pole radius of the IIR prototype NFs. The suggested multi NF can also be adapted to eliminate second‐, third‐ and fourth‐order harmonics of periodic noise besides the fundamental noise frequency component. A special case when two notch frequencies ω₁ and ω₂ are such that [(cosω₁)(cosω₂) = ? 1/2] has also been discussed. The IIR multi NF design for this special case results in reduction of the number of multipliers without affecting the response of the desired NF. For the aforereferred condition, the required coefficients of impulse response of FIR multi notch filter get reduced to almost half in number resulting in reduced computations. The number of zero coefficients further reduces with increase in ‘r’ value. In addition, the frequency response becomes better, with reduced ripples in the pass bands, when ‘r’ is increased and length ‘L’ of the FIR NF is chosen appropriately. Copyright © 2010 John Wiley & Sons, Ltd.