Synchrosqueezed windowed linear canonical transform: A method for mode retrieval from multicomponent signals with crossing instantaneous frequencies

2025/10/12 by Li, Shuixin, Chen, Jiecheng, Jiang, Qingtang +1
#FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2510.10438

Abstract

In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing this problem is to introduce an additional chirprate parameter and use the chirplet transform (CT) to elevate the two-dimensional time-frequency representation to a three-dimensional time-frequency-chirprate representation. From a certain point of view, the CT of a signal can be regarded as a windowed special linear canonical transform of that signal, undergoing a shift and a modulation. In this paper, we develop this idea to propose a novel windowed linear canonical transform (WLCT), which provides a new time-frequency-chirprate representation. We discuss four types of WLCTs. In addition, we use a special X-ray transform to further sharpen the time-frequency-chirprate representation. Furthermore, we derive the corresponding three-dimensional synchrosqueezed transform, demonstrating that the WLCTs have great potential for three-dimensional signal separation.

Citations

• Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies
• Analysis of a Direct Separation Method Based on Adaptive Chirplet Transform for Signals with Crossover Instantaneous Frequencies
• Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application
• Theory and applications of short-time linear canonical transform
• Time-Scale-Chirp_rate Operator for Recovery of Non-stationary Signal Components with Crossover Instantaneous Frequency Curves
• Analysis of an Adaptive Short-Time Fourier Transform-Based Multicomponent Signal Separation Method Derived from Linear Chirp Local Approximation
• A Chirplet Transform-based Mode Retrieval Method for Multicomponent Signals with Crossover Instantaneous Frequencies
• Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
• Lens-System Diffraction Integral Written in Terms of Matrix Optics*

Related

• Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies
• Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application
• A Chirplet Transform-based Mode Retrieval Method for Multicomponent Signals with Crossover Instantaneous Frequencies
• High-Order Synchrosqueezed Chirplet Transforms for Multicomponent Signal Analysis
• High-resolution chirplet transform: from parameters analysis to parameters combination