| nfinite Impulse Response (IIR) adaptive notch filtering is a relatively new method for use in sinusoidal retrieval, which encompasses frequency acquisition, line enhancement and line suppression. In this regard, there needed to be further exploration and an increased understanding of this technique in order to improve on existing algorithms. A disadvantage of available algorithms which use adaptive notch filtering is the inability to obtain rapid convergence while simultaneously requiring low computation.;An algorithm is proposed that has fast convergence with extremely low computational complexity; therefore, it is suitable for practical applications. The development of this algorithm arose from the fact that stochastic Gauss-Newton type methods are known to have faster convergence and better statistical properties than the well-known stochastic gradient or least-mean-square (LMS) algorithm. An analysis is performed in order to substantiate the validity of the simplification made to develop such an algorithm. The result is a cascade form adaptive notch filter of quadratic performance at linear cost. Specifically, the computational complexity reduces from O(;General analytical results in this area are applicable to a selected category of algorithms. Here, it is shown that for a first-order pseudolinear regression (PLR) type system, the bias is asymptotically negligible. By using a direct approach of analysis, this result is shown to hold for the recursive prediction error method (RPEM) also. Computer simulations are presented which verify the analytical expressions developed.;In concurrence with developing computationally efficient cascade adaptive notch filters, a new structure for implementing an adaptive filter is introduced. This tree type structure reduces the inherent quadratic complexity for computing the gradient in a cascade formulation to... |
