Time-frequency characteristics estimation of underwater moving objects using memory-dependent derivative method

The line-spectra changes of the radiated noise of underwater moving object is observed as the form of narrow-band time varying signal due to the Doppler effect. The modulation law of the time varying signal contains a large number of feature information of moving targets, which can be used for detection and classification. The goal of time-frequency analysis is to extract subtle changes the function relationship of frequency over time. In this research, a memory-dependent derivative methodology is proposed to deal with accurate time–frequency representation of time varying signals under strong background noise. Memory-dependent derivative is a convolution of a common derivative by the time-varying signals with a dynamic weighted function in the past period time. Considering the stated methodology, it is derived that the discrete data from previous times to estimate signal value at current time and reduce the effects of the noise. Using the Fourier transformation with different scales and delays transformation as the kernel function, the energy concentrated time-frequency curve is obtained with higher resolution and without frequency leakage. The simulated results demonstrate that given method is immune to background noise and estimate the main frequencies with high accuracy, specially the rapid change of the modulated frequency.