Matched power-frequency-modulated signal transform and its application in bat call signal analysis

Bat call signal analysis is an important research topic, which is meaningful for bat species identification, and the design of various biomimetic systems. In addition to the commonly used methods in the time-frequency domain, the fractional Fourier transform (FRFT) is a valuable signal processing tool, as it is a generalization of the Fourier transform. However, the FRFT is constrained to the analysis of the linear frequency modulated-like bat call signal, while the modulation of the harmonics in a bat call is often nonlinear. For this reason, this paper proposes an integral transform, named matched power-frequency-modulated (PFM) signal transform (MPST), which is also the generalization of the Fourier transform, more precisely, a time-warping Fourier transform. As with the limitation of FRFT, the MPST is constrained to the analysis of the PFM-like bat call with the instantaneous frequency defined as an approximate power function abut time, in which the power can be an arbitrary positive integer or a fraction. The applications of MPST on the PFM-modeled bat call analysis are mainly parameter estimation and harmonic separation, and the performance is fully validated using the recordings of the feeding buzzes, social calls, and distress calls from the European bats.