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 f0 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 f0 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 f0 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 0 dB. 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 f0, 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.