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Many speech and music analysis and processing schemes rely on an estimate ofthe fundamental frequency $f_0$ of periodic signal components. Most establishedschemes apply rather unspecific signal models such as sinusoidal models to theestimation problem, which may limit time resolution and estimation accuracy.This study proposes a novel time-domain locked-loop algorithm with lowcomputational effort and low memory footprint for $f_0$ estimation. The loopcontrol signal is directly derived from the input time signal, using a harmonicsignal model. Theoretically, this allows for a noise-robust and rapid $f_0$estimation for periodic signals of arbitrary waveform, and without therequirement of a prior frequency analysis. Several simulations with shortsignals employing different types of periodicity and with added wide-band noisewere performed to demonstrate and evaluate the basic properties of the proposedalgorithm. Depending on the Signal-to-Noise Ratio (SNR), the estimator wasfound to converge within 3-4 signal repetitions, even at SNR close to or below0dB. Furthermore, it was found to follow fundamental frequency sweeps with adelay of less than one period and to track all tones of a three-tone musicalchord signal simultaneously. Quasi-periodic sounds with shifted harmonics aswell as signals with stochastic periodicity were robustly tracked. Mean andstandard deviation of the estimation error, i.e., the difference between trueand estimated $f_0$, were at or below 1 Hz in most cases. The results suggestthat the proposed algorithm may be applicable to low-delay speech and musicanalysis and processing.

The Period-Modulated Harmonic Locked Loop (PM-HLL): A low-effort algorithm for rapid time-domain multi-periodicity estimation