A Novel Design of Sparse FIR Multiple Notch Filters with Tunable Notch Frequencies

We focus on the design of finite impulse response (FIR) multiple notch filters. To reduce the computational complexity and hardware implementation complexity, a novel algorithm is developed based on the mixture of the tuning of notch frequencies and the sparsity of filter coefficients. The proposed design procedure can be carried out as follow: first, since sparse FIR filters have lower implementation complexity than full filters, a sparse linear phase FIR single notch filter with the given rejection bandwidth and passband attenuation is designed. Second, a tuning procedure is applied to the computed sparse filter to produce the desired sparse linear phase FIR multiple notch filter. When the notch frequencies are varied, the same tuning procedure can be employed to render the new multiple notch filter instead of designing the filter from scratch. The effectiveness of the proposed algorithm is demonstrated through three design examples.