Adaptive detection and enhancement of multiple sinusoids using a cascade IIR filter

A constrained adaptive IIR (infinite-impulse-response) filter consisting of a cascade of biquadratic notch sections is used to track multiple sinusoids. The structure can be used to isolate individual sinusoids. It is shown that, for small changes around the optimum solution, the proposed update algorithm approximates the Gauss-Newton update without requiring a matrix inversion. Furthermore, the transient response is approximately independent of the number of sinusoids or their power levels. Important adaptive line enhancement performance criteria such as signal-to-noise improvement ratio and the bias in the frequency estimate assuming white noise are derived for the single-sinusoid case.<>