A study on phase recovery processing of nonlinear signals based on STFT

Abstract

Nonlinear signals are widely used in the field of mechanical vibration, communication modulation, and transient detection. Their phase trajectories vary with time and are closely related to local frequency, amplitude-envelope variation, and burst-energy distribution. To address phase recovery difficulty, a short-time Fourier transform (STFT) method is proposed to recover nonlinear signals in a phase-constrained manner and is evaluated using polynomial frequency-modulated, AM–FM coupled, and transient impulse signals. The STFT is used to extract the time-frequency amplitude spectrum, and amplitude-consistency projection, inter-frame phase-continuity constraints, low-energy frequency-point masking, and a time-domain consistency iteration mechanism are used to estimate the phase spectrum and reconstruct the signal. Across 20 independent initializations, the proposed method achieved NRE values of 0.061 ± 0.004, 0.069 ± 0.005, and 0.084 ± 0.006 and PMSE values of 0.092 ± 0.007, 0.107 ± 0.008, and 0.136 ± 0.010 for the three nonlinear signal classes. The improvements over Weighted GLA were statistically significant. Ablation analysis showed that inter-frame phase continuity made the largest contribution to reconstruction accuracy, whereas adaptive step-size decay mainly improved convergence efficiency. Additional multi-component experiments confirmed that the method retained an advantage under ridge interference, although reconstruction accuracy decreased as spectral overlap increased.