Parameterized Frequency Synchronous Time-Frequency Concentrated Transform

There is a class of multi-component amplitude modulation and frequency modulation (AM-FM) signals with a common instantaneous frequency (IF) change trend in the real world. For example, vibration signals from rotating machinery, sound signals, and biomedical signals, etc. These signals have close IFs and are generally subject to various noise interferences. The current methods are unable to effectively handle this type of signals affected by strong noise interference. The obtained time-frequency representation (TFR) has low resolution and weak energy concentration. To solve these problems, we propose a novel parameterized frequency synchronous time-frequency concentrated transform (PFTCT) in this paper. We constructed new frequency synchronous parameterized demodulation operator and shift operator to match the variation pattern of IF for each sub-signal simultaneously. And PFTCT innovatively derives unbiased IF estimation operator with frequency synchronization, which concentrates the main energy of TFR on the signal’s IF trajectory. Moreover, we developed a fast method for calculating PFTCT based on fast Fourier transform, which significantly improves computational efficiency. To filter out strong noise interference, PFTCT iteratively optimizes the kernel function parameters and gradually obtain appropriate parameters. We conducted some complex simulated and experimental signals processing experiments under strong noise to validate proposed PFTCT. The results indicate that the proposed method can obtain high-resolution TFRs and accurately display the signal’s IF trajectory. Moreover, the proposed method is superior to current time-frequency transform methods.