Constrained RLS algorithm for narrow band interference rejection from EEG signal during CES

The filtering of signals in the presence of a narrow-band interference noise is a common problem in biomedical signal processing. A double adaptive band-rejection filter is applied to an electroencephalographic (EEG) signal corrupted by a double narrow-band white Gaussian noise during cranial electrical stimulation (CES). The multiple adaptive IIR digital band-rejection filters are designed by the pole-zero placement on the unit circle method using a unique second-order filter structure. Multiple band-rejection filters (of order 2N) can be designed by cascading N second-order band-rejection filters. The coefficients of the multiple band-rejection filters are calculated by convoluting the coefficients of the second-order band-rejection filters. The pole-zero placement on the unit circle method relates the coefficients of the filter through fundamental coefficients that are assumed to be independent. These coefficients are updated through the recursive least-squares (RLS) algorithm. Unlike other RLS based multiple adaptive band-rejection filters, the new constrained RLS (CRLS) multiple adaptive HR band-rejection filter truly adapts its zeros and poles.