Nonlinear squeezing time-frequency transform for weak signal detection

Conventional time-frequency analysis methods can characterize the time-frequency pattern of multi-component nonstationary signals. However, it is difficult to detect weak components hidden in complex signals because the time-frequency representation is influenced by the signal amplitude. In this paper, a novel algorithm called nonlinear squeezing time-frequency transform (NSTFT) is proposed to characterize the time-frequency pattern of multi-component nonstationary signals. Most importantly, theoretical analysis shows that the NSTFT method is independent of the signal amplitude and is only relevant to the signal phase, thus it can be used for weak signal detection. Moreover, an improved ridge detection algorithm is proposed in this paper for instantaneous frequency estimation. The experiments on simulated and real-world signals show that the NSTFT method can effectively detect weak components in complex signals, and the comparison study with some other time-frequency analysis methods also shows the advantages of the NSTFT method in weak signal detection.