Instantaneous fundamental frequency estimation of non-stationary periodic signals using non-linear recursive filters

This paper presents an algorithm for estimating the instantaneous fundamental frequency of a noisy non-stationary periodic signal whose components are harmonically related. To this end, the authors´ propose a harmonic state-space model for the input signal and use it to derive an extended Kalman filter (EKF), an unscented Kalman filter (UKF) and a particle filter (PF). In this model, the input signal is characterised by a time-varying fundamental frequency and amplitude which is a practical assumption for real-world periodic signals. In contrast to most of existing methods such as short-time Fourier transform, the proposed algorithm does not use any windowing technique. Therefore the trade-off between time and frequency resolutions is less controversial and so can be used for real-time frequency tracking. It also reveals some fine and continuous variations in signal pitch such as Vibrato and Glissando. Simulation results show that the proposed algorithm performs well even when most of the signal energy is contained in the higher-order harmonics. The performance of the proposed algorithm using EKF, UKF and PF is also evaluated and the results are compared in diverse conditions.