Harmonic signal modeling using adaptive nonlinear function estimation

It is well-known that sine waves produce harmonic overtones when passed through static nonlinear functions. This paper describes a new algorithm where an arbitrary periodic signal is estimated recursively. The estimated signal model is typically parameterised as a real sine wave with unknown frequency in cascade with a piecewise linear function. A recursive Gauss-Newton prediction error identification algorithm for joint estimation of the driving frequency and the parameters of the nonlinear output function can then be derived. The approach handles colored measurement disturbances and gives a direct measure of the size of the nonlinearity that corresponds to the harmonic spectrum. The Cramer-Rao bound (CRB) is also calculated in the paper