Wideband Lv's Distribution: A signal processing tool for hyperbolic frequency modulated signal analysis

Linear frequency modulated (LFM) and hyperbolic frequency modulated (HFM) signals are employed in many areas, especially in the echolocating systems. To solve the problem of signal detection and estimation, various integral transforms have been designed for the LFM signal, such as fractional Fourier transform, Lv's distribution (LVD), and so on. However, there is no transform directly used for that of the HFM signal so far. LVD is a good option for the detection and estimation of the LFM signal, but not for that of the HFM signal, because of model mismatching. Inspired by LVD, the wideband Lv's distribution (WLVD) is proposed, capable of transforming the HFM signal into two-dimensional peaks, and obtaining the parameters of each component according to the peak position in the "delay-scale" domain. This above ability is accomplished in two steps. Firstly, a time-scaling (TS) operation is performed on the wideband ambiguity function of the HFM signal to correct the spectral peak migration, and then the inverse Fourier transform is calculated along the corrected "ridge". As a signal analysis tool, the WLVD exhibits the same advantage as LVD, i.e. the cross-terms of the multi-component signal have little effect, despite the quadratic function of the signal spectrum dealt with. The experiment results for the simulated and real signals demonstrate the significant potential of WLVD, owing to the widespread application of HFM signals across radar, sonar, and even some echolocating mammals.