论文标题
定义几乎谐波信号的基本频率
Defining Fundamental Frequency for Almost Harmonic Signals
论文作者
论文摘要
在这项工作中,我们考虑了几乎但不是完全谐波的信号的建模,即由正弦曲线组成,其频率接近是通用频率的整数倍数。通常,在应用中,尽管信号实际上并非周期性,但这些信号被视为完全谐波,可以估算其基本频率。本文中,我们为这种非族人信号提供了三个不同的定义,对基本频率的概念进行了研究,并研究了不同选择在建模和估计中的含义。我们表明,其中一个定义对应于错误的指定建模方案,并提供了一个理论基准,用于分析在完全谐波假设下得出的估计器的行为。第二个定义源于最佳的质量传输理论,并根据信号的光谱特性得出了基本频率的强大且易于解释的概念。第三个定义将无谐信号解释为对随机扰动的谐波信号的观察。这允许计算有关估计性能的混合信息理论界限,以及找到达到界限的估计器。使用数值示例说明了理论发现。
In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. Typically, in applications, such signals are treated as perfectly harmonic, allowing for the estimation of their fundamental frequency, despite the signals not actually being periodic. Herein, we provide three different definitions of a concept of fundamental frequency for such inharmonic signals and study the implications of the different choices for modeling and estimation. We show that one of the definitions corresponds to a misspecified modeling scenario, and provides a theoretical benchmark for analyzing the behavior of estimators derived under a perfectly harmonic assumption. The second definition stems from optimal mass transport theory and yields a robust and easily interpretable concept of fundamental frequency based on the signals' spectral properties. The third definition interprets the inharmonic signal as an observation of a randomly perturbed harmonic signal. This allows for computing a hybrid information theoretical bound on estimation performance, as well as for finding an estimator attaining the bound. The theoretical findings are illustrated using numerical examples.