ABSTRACT

This chapter designs the adaptive filters that are signal environments consisting of sinusoidal components of unknown frequency immerged in background noise. It reviews background material which introduces the ideal notch filter and its relation to determining signal frequencies by seeking the minimum point of a cost function. The chapter also reviews the direct form and lattice approximations to the ideal notch filter, using second-order filter sections. It pursues adaptation algorithm design for the two notch filter approximations. The chapter shows a simplified adaptation algorithm for the lattice formulation, which features faster convergence properties than the gradient descent formulation. It reviews the input signal model, the ideal notch filter, and a cost function whose minimum point forces the notch filter to identify one of the input signal frequencies. The chapter considers the single sinusoid case to simplify the presentations. It reviews two candidate approximations to the ideal notch filter, corresponding respectively to the direct form filter and the lattice filter.