The amplitude and phase estimation of a sinusoid (APES) method, receiving superior results to conventional Fourier transform (FT) featured as narrower spectral peaks and lower side-lobe levels, has been widely applied in the fields of medical imaging, remote sensing, synthetic aperture radar, etc. Both FT and APES suppose the signal collected is stationary. When handing with non-stationary signals, we have to resort to the adaptive extension of FT, i.e., the short time Fourier transform (STFT). Likewise, we also need to extend APES to adapt to changing signal spectrum while maintaining the advantage of high-resolution. To this end, this paper proposes a block-wise recursive APES (BRAPES) method for online spectral estimation of time-varying signals, in which the size of the updating block is adjustable to accommodate the real-time requirement of online computing. Additionally, inspired by recent developments in reassignment method (RM) and synchrosqueezing transform (SST) against the Heisenberg uncertainty principle, we construct a frequency-squeezing postprocessing (FSP) technique aiming at improving the concentration of time–frequency (TF) representation by BRAPES, which essence is to move the spectral lines towards the nearest natural frequency rather than changing the amplitude. The numerical examples demonstrate that the proposed approach, BRAPES aided with FSP (BRAPES-FSP), not only has high accuracy in processing nonstationary signals, but also can adopt a much shorter data sequence for analysis than Fourier class methods, which greatly guarantee the real-time performance of computation in online environment. Furthermore, we employ BRAPES-FSP to process the acceleration responses of cables of a real cable-stayed bridge and a experimental cable in workshop, proving its capability and potential of dealing with vibration monitoring signals in such fields as structural health monitoring.

正弦波（APES）方法的幅度和相位估计具有比传统傅里叶变换（FT）更好的结果，具有更窄的频谱峰值和更低的旁瓣电平，已广泛应用于医学成像、遥感、合成等领域。孔径雷达等。FT 和 APES 都假设收集的信号是静止的。在处理非平稳信号时，我们不得不求助于 FT 的自适应扩展，即短时傅立叶变换 (STFT)。同样，我们还需要扩展 APES 以适应不断变化的信号频谱，同时保持高分辨率的优势。为此，本文提出了一种分块递归APES（BRAPES）方法，用于时变信号的在线谱估计，其中更新块的大小是可调的，以适应在线计算的实时性要求。此外，受重新分配方法 (RM) 和同步压缩变换 (SST) 针对海森堡不确定性原理的最新发展的启发，我们构建了一种频率压缩后处理 (FSP) 技术，旨在提高 BRAPES 的时频 (TF) 表示的集中度，其本质是将谱线移向最近的自然频率，而不是改变幅度。数值算例表明，所提出的BRAPES辅助FSP（BRAPES-FSP）方法不仅在处理非平稳信号方面具有较高的精度，而且可以采用比傅立叶类方法更短的数据序列进行分析，极大地保证了在线环境下计算的实时性。此外，我们使用BRAPES-FSP处理了真实斜拉桥和车间实验索的加速度响应，证明了其在结构健康监测等领域处理振动监测信号的能力和潜力。