增强的时频表示和模态分解
Enhanced Time-Frequency Representation and Mode Decomposition
摘要：
时频表示（TFR）允许模式重构在解释和分析由各种模式组成的非平稳信号中起着重要的作用。然而，这是困难的，大多数以前的方法来处理信号模式与紧密间隔或频谱重叠的瞬时频率（IF），特别是在恶劣的环境。为了解决这个问题，我们提出了一种增强的TFR和模式分解（ETFR-MD）的方法，这是特别适合于表示和分解多模信号的低信噪比（SNR）条件下的接近或交叉的IF。提出的ETFR-MD的重点放在精确的IF和瞬时幅度（IA）提取的基础上的每一个信号模式的短时傅里叶变换（STFT）。首先，我们设计了一个初始的IF估计方法，专门用于涉及交叉IF的情况。此外，提出了一种低复杂度的模式增强方案，使增强的IF更好地适应潜在的IF法律。最后，从信号的STFT系数中提取IA与增强的IF相结合，使我们能够重建每个信号模式。此外，我们推导出数学表达式，揭示了我们的方法的最佳窗口长度和分离干扰。ETFR-MD与已有的相关方法兼容，因此可以被视为向更通用的时频表示和分解方法迈出的一步。实验结果证实了ETFR-MD与最先进的基准相比具有卓越的性能。
英文摘要：
Time-frequency representation (TFR) allowing for mode reconstruction plays a significant role in interpreting and analyzing the nonstationary signal constituted of various modes. However, it is difficult for most previous methods to handle signal modes with closely-spaced or spectrally-overlapped instantaneous frequencies (IFs) especially in adverse environments. To address this issue, we propose an enhanced TFR and mode decomposition (ETFR-MD) method, which is particularly adapted to represent and decompose multi-mode signals with close or crossing IFs under low signal-to-noise ratio (SNR) conditions. The emphasis of the proposed ETFR-MD is placed on accurate IF and instantaneous amplitude (IA) extraction of each signal mode based on short-time Fourier transform (STFT). First, we design an initial IF estimation method specifically for the cases involving crossing IFs. Further, a low-complexity mode enhancement scheme is proposed so that enhanced IFs better fit underlying IF laws. Finally, the IA extraction from signal's STFT coefficients combined with the enhanced IFs enables us to reconstruct each signal mode. In addition, we derive mathematical expressions that reveal optimal window lengths and separation interference of our method. The proposed ETFR-MD is compatible with previous related methods, thus can be regarded as a step toward a more general time-frequency representation and decomposition method. Experimental results confirm the superior performance of the ETFR-MD when compared to a state-of-the-art benchmark.
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