Accurate time-frequency estimation in sαs noise via memory-dependent derivative

Abstract

This letter presents a time-frequency estimation approach based on memory-dependent derivative to obtain accurate spectrograph interpolation information. The memory correlation derivative is the convolution of a time-varying signal with a dynamic weighting function over a past time period with respect to a common derivative. Considering the described method, discrete data from previous times can be derived to estimate the signal values at the current time and to reduce the effect of noise. Fourier transforms with different scales and delay transforms are used as kernel functions to obtain energy-concentrated time-frequency curves with higher resolution and without frequency leakage. Besides, the memory-dependent derivative with adjustable scale factor is used to overcome time-frequency grid mismatches. Furthermore, differing from the phase accumulation manner of conventional time-frequency estimation, ℓ1-norm suppresses the heavy-tailed effect from outliers, thus the robustness of estimator can be enhanced greatly. By suitably choices of scale factor, the estimator can be tuned to exhibit high resolution in targeted regions of the time-frequency spectrum.