Reported is a three-step procedure (also referred to as the observer) for fast and unbiased determination of the dominant frequencies and amplitude of thermoacoustic oscillations. The first step is to determine the rang of the dominant frequency by computing the amplitude at frequency bins uniformly distributed from the lowest possible frequency to the Nyquist frequency (i.e., one-half of the sampling frequency) with a strategically specified, widely spaced frequency-bin separation. The other steps are to refine the estimation. The frequency estimation becomes unbiased after step 2, and the error (or uncertainty) is insensitive to the signal-to-noise ratio. The computational complexity can be orders-of-magnitude lower than the discrete Fourier transform and the fast Fourier transform, and the accuracy is no longer limited by $F_s/N$, where $F_s$ and $N$ refer to the sampling frequency and the data length, respectively. This Paper recommends that the frequencies and amplitude be estimated every two pressure cycles. Cycle-to-cycle (or short-term) variations in the frequencies and amplitude are well resolved for thermoacoustic oscillations in three different real devices exhibiting quasi-steady oscillations before the onset of combustion instabilities and spontaneous instabilities (i.e., linearly unstable oscillations) with different levels of nonlinearities, respectively.

报告了一种三步过程（也称为观察者），用于快速，无偏地确定主频率和热声振荡的幅度。第一步是通过以策略性指定的，间隔较大的频率计算从最低的可能频率到奈奎斯特频率（即采样频率的一半）均匀分布的频点处的幅度，从而确定主导频率的范围，箱分离。其他步骤是完善估计。频率估算在步骤2之后变得无偏，并且误差（或不确定性）对信噪比不敏感。计算复杂度可以比离散傅立叶变换和快速傅立叶变换低几个数量级，并且精度不再受以下因素的限制$F_s/ñ$，在哪里 $F_s$ 和 $ñ$分别指采样频率和数据长度。本文建议每两个压力周期估算一次频率和振幅。在出现燃烧不稳定性和自发不稳定性（即线性不稳定振荡​​）之前，三个不同的表现出准稳态振荡的真实设备中的热声振荡，可以很好地解决频率和幅度的逐周期（或短期）变化。不同程度的非线性。