Synchrosqueezing-Based Demodulation Transform for Analyzing Complicated Signal Containing Strong Noise

A large number of nonstationary amplitude modulation-frequency modulation (AM-FM) signals exist in the actual engineering field. Time-frequency analysis (TFA) is a powerful approach for handling AM-FM signals. However, there is still room for improvement in existing methods to reveal the time-frequency changing characteristics of complicated AM-FM signals. Especially for signals with overlapping IF trajectories or adjacent IF trajectories. Moreover, the current TFA methods are prone to strong noise interference. To tackle these issues, we propose a novel TFA method called synchrosqueezing-based demodulation transform (SSDT) for analyzing complex nonstationary signals containing strong noise in this article. SSDT introduces the idea of synchronous squeezing extraction into demodulation transform. First, SSDT optimizes the calculation formulas of the demodulation transform by adding instantaneous time variables to the demodulation factor, shift factor, and frequency basis function. And SSDT adopts kernel function parameters that match the signal’s time-varying properties. Then, SSDT derives a high-precision instantaneous frequency (IF) estimation operator to further concentrate the core energy of time-frequency representation (TFR) at the signal’s IF trajectory. In this way, SSDT can effectively extract the signal’s instantaneous variation features and improve the energy-focusing performance of TFR. To obtain correct parameters, SSDT iteratively optimizes the kernel function parameters, gradually matching the signal’s IFs, which can suppress strong noise interference. To verify SSDT, some signal processing experiments were conducted using complex simulations and real signals containing strong noise. The experimental results display that SSDT can effectively handle complicated strong noisy signals with adjacent IFs, crossing IFs, and fast-changing IFs. SSDT can obtain more accurate TFR than other commonly used TFA methods. The TFR of SSDT can more accurately display the IF trajectory and has a stronger energy concentration.