多成分信號分析之高階同步壓縮 Chirplet 轉換

Abstract

本研究專注於分析具有重疊瞬時頻率（IF）的多成分信號。傳統方法，如短時傅立葉變換（STFT）、經驗模態分解（EMD）等，將在目標信號具有重疊瞬時頻率時失效，因為無法將信號適當地分解。這個問題最初是利用 chirplet轉換（CT）來解決的，然而，由於重疊部分的能量衰減速率較低，導致會有顯著的交叉項的影響，因此添加其他步驟是必要的。通過加入同步擠壓步驟，即同步擠壓chirplet轉換（SCT），可以使時頻-啁啾空間中的能量更加聚集。雖然SCT在啁啾信號的疊加中表現良好，但我們發現它在高啁啾變化率的信號上出現錯誤，這是由於對瞬時頻率的錯誤估計。相對應地，信號的曲線在某個時間點斷裂，這意味著能量不夠集中。在本文提出了對 CT的後處理的改進，主要目標是修正 SCT中引入的估計，並進行高階同步擠壓 chirplet轉換。所提出的方法在面對啁啾變化率更大的多成分信號時減少了錯誤的估計。提供了新的重新分布運算子的理論分析，包括表示的每個導數的近似值和成分的點估計。提出了一些高啁啾變化率合成信號的數值實驗，以驗證所提出的高階SCT的有效性。

This research centers on analyzing signals that contain multiple components with overlapping instantaneous frequencies (IF). The classic method, like the short-time Fourier transforms (STFT), empirical modes decomposition (EMD), etc, will be illness when the target signals have the overlapping IF as one can not separate the signal properly. This problem was initially solved with the chirplet transform (CT), however, due to the low rate of decay at the cross part, the effect of the cross terms is obvious, so adding the other technique is necessary. By adding the synchrosqueezing step, which is called the synchrosqueezed chirplet transform (SCT), the ridge of the representation in time-frequency-chirp space can be sharpened. Although the SCT performed well in the superposition of the chirp signal, we found that it went wrong with the high chirp modulation signal due to the incorrect estimation of the IF. The curve corresponding to the signal collapses at some time instant, which means that the energy is not concentrated enough. In this paper, we present enhancements to the post-transformation of the Chirplet Transform (CT). The primary objective is to refine the estimation introduced in the Synchrosqueezed Chirplet Transform (SCT) and implement the high-order synchrosqueezed chirplet transform. The proposed method mitigates estimation errors when dealing with a wider range of chirp-modulated multi-component signals. The theoretical analysis of the new reassignment ingredients is provided, including the approximation of each derivative of the representation, and the point estimate of the ingredients. Numerical experiments on high chirp modulation synthetic signals are conducted to validate the effectiveness of the proposed high-order Synchrosqueezed Chirplet Transform (HSCT).