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

Abstract

Many speech and music analysis and processing schemes rely on an estimate of the fundamental frequency $f_0$ of periodic signal components. Most established schemes apply rather unspecific signal models such as sinusoidal models to the estimation problem, which may limit time resolution and estimation accuracy. This study proposes a novel time-domain locked-loop algorithm with low computational effort and low memory footprint for $f_0$ estimation. The loop control signal is directly derived from the input time signal, using a harmonic signal model. Theoretically, this allows for a noise-robust and rapid $f_0$ estimation for periodic signals of arbitrary waveform, and without the requirement of a prior frequency analysis. Several simulations with short signals employing different types of periodicity and with added wide-band noise were performed to demonstrate and evaluate the basic properties of the proposed algorithm. Depending on the Signal-to-Noise Ratio (SNR), the estimator was found to converge within 3-4 signal repetitions, even at SNR close to or below 0dB. Furthermore, it was found to follow fundamental frequency sweeps with a delay of less than one period and to track all tones of a three-tone musical chord signal simultaneously. Quasi-periodic sounds with shifted harmonics as well as signals with stochastic periodicity were robustly tracked. Mean and standard deviation of the estimation error, i.e., the difference between true and estimated $f_0$, were at or below 1 Hz in most cases. The results suggest that the proposed algorithm may be applicable to low-delay speech and music analysis and processing.