Adaptive Scaling Demodulation Transform: Algorithm and Applications

Classic postprocessing time–frequency analysis (TFA) methods calculated by the short-time Fourier transform (STFT) suffer from the problems of blurry cross points and unsatisfied time–frequency concentration under noise interference. For solving the problems, a novel TFA technique, termed adaptive scaling demodulation transform (ASDT), is developed in this article. The ASDT aims to calculate ideal time–frequency representation (TFR) by adaptively estimating the instantaneous frequency (IF) curves, extracting the time–frequency amplitudes at the estimated IF curves, and reassigning these time–frequency amplitudes into a new TFR. The IF curves are adaptively estimated by constructing the scaling demodulation operator and maximum criterion of local spectrum amplitude. The time–frequency amplitudes at the calculated IF curves are selected from the STFT result. In this way, the ASDT can eliminate smeared time–frequency amplitudes and background noise and accurately characterize intersecting frequency ridges with high energy concentration. The effectiveness of the developed technique is verified through simulated signal and two different mechanical vibration signals. Comparison analysis with classic TFA techniques shows that the ASDT has much better ability for processing signal with intersecting frequency curves under noise interference.