Sparse FIR notch filter design and its application

A technique for designing a sparse FIR notch filter is presented. First, a sparse property of the ideal notch filter, whose notch frequency has the form (q/2p)π is derived, where p and q are coprime integers. Then, the Lagrange multiplier method is used to obtain the coefficients of the sparse notch filter which is optimal in the least-squares sense. Next, a design example is presented to demonstrate the effectiveness of this approach. Finally, a sparse notch filter is applied to eliminate the 60 Hz powerline interference superimposed on the electrocardiogram signals