Enhanced Time-Frequency Representation and Mode Decomposition

TL;DR

This paper introduces ETFR-MD, an advanced method for time-frequency representation and mode decomposition that effectively handles closely-spaced or crossing instantaneous frequencies in noisy environments, improving signal analysis accuracy.

Contribution

The paper presents a novel ETFR-MD approach with specialized initial IF estimation, mode enhancement, and IA extraction techniques for better decomposition of multi-mode signals with overlapping frequencies.

Findings

ETFR-MD outperforms existing methods in noisy conditions.

Accurate extraction of IF and IA for crossing frequencies.

Mathematical analysis guides optimal window selection.

Abstract

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.