A minimal parameter adaptive notch filter with constrained poles and zeros

A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broadband process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of proper infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the algorithm approaches the Cramer-Rao bound in estimating the frequencies of the sine wave signals.