A novel wavelet-based notch filter with controlled null width

This paper presents a wavelet-based approach for the design of the finite impulse response (FIR) notch filter with controlled null width. The M-band P-regular wavelet filters are employed to constitute the null space of the derivative constraint matrix. Taking advantage of the vanishing moment property of the wavelet filters, the proposed method controls the null width of the notch filter by adjusting the regularity of the employed wavelet filters. Besides, the selection of large number of bands of the wavelet filters can effectively reduce the minimum mean square error and thus improve the performance of the notch filter. Computer simulations show that, in addition to possessing lower computational complexity, the proposed reduced-rank method has similar frequency response compared to those of the full-rank-based techniques.