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The Period-Modulated Harmonic Locked Loop (PM-HLL): A low-effort algorithm for rapid time-domain periodicity estimation
arXiv - CS - Sound Pub Date : 2021-07-14 , DOI: arxiv-2107.06645 Volker Hohmann
arXiv - CS - Sound Pub Date : 2021-07-14 , DOI: arxiv-2107.06645 Volker Hohmann
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
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 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.
中文翻译:
周期调制谐波锁定环 (PM-HLL):一种用于快速时域周期性估计的省力算法
许多语音和音乐分析和处理方案依赖于对周期信号分量的基频 f0 的估计。大多数已建立的方案将相当不特定的信号模型(例如正弦模型)应用于估计问题,这可能会限制时间分辨率和估计精度。本研究提出了一种新颖的时域锁环算法,用于 f0 估计,具有低计算量和低内存占用。回路控制信号直接从输入时间信号中导出,使用谐波信号模型。从理论上讲,这允许对任意波形的周期信号进行抗噪声和快速 f0 估计,并且不需要事先进行频率分析。对采用不同类型周期性和添加宽带噪声的短信号进行了几次模拟,以证明和评估所提出算法的基本特性。根据信噪比 (SNR),发现估计器在 3-4 次信号重复内收敛,即使 SNR 接近或低于 0dB。此外,发现它以小于一个周期的延迟跟踪基频扫描,并同时跟踪三音音乐和弦信号的所有音调。具有偏移谐波的准周期性声音以及具有随机周期性的信号被稳健地跟踪。在大多数情况下,估计误差的平均值和标准偏差,即真实和估计 f0 之间的差异,等于或低于 1 Hz。
更新日期:2021-07-15
中文翻译:
周期调制谐波锁定环 (PM-HLL):一种用于快速时域周期性估计的省力算法
许多语音和音乐分析和处理方案依赖于对周期信号分量的基频 f0 的估计。大多数已建立的方案将相当不特定的信号模型(例如正弦模型)应用于估计问题,这可能会限制时间分辨率和估计精度。本研究提出了一种新颖的时域锁环算法,用于 f0 估计,具有低计算量和低内存占用。回路控制信号直接从输入时间信号中导出,使用谐波信号模型。从理论上讲,这允许对任意波形的周期信号进行抗噪声和快速 f0 估计,并且不需要事先进行频率分析。对采用不同类型周期性和添加宽带噪声的短信号进行了几次模拟,以证明和评估所提出算法的基本特性。根据信噪比 (SNR),发现估计器在 3-4 次信号重复内收敛,即使 SNR 接近或低于 0dB。此外,发现它以小于一个周期的延迟跟踪基频扫描,并同时跟踪三音音乐和弦信号的所有音调。具有偏移谐波的准周期性声音以及具有随机周期性的信号被稳健地跟踪。在大多数情况下,估计误差的平均值和标准偏差,即真实和估计 f0 之间的差异,等于或低于 1 Hz。