Methods to segment CF and FM components of a call?

Question

I have single-channel recordings of horseshoe/rhinolophid bats which have call shapes with a 'tabletop' or 'staple-pin' shape. (See spectrogram below). The flat portion is the 'constant-frequency' part (CF), and the modulated section is the 'frequency modulated' part (FM). Such calls are thus called CF-FM calls in the bat literature.

Spectrogram of a CF-FM bat call recorded in a cave. X-axis in seconds.

I'd like to accurately separate the FM 'legs' from the flat CF component. After separation I'd like to measure component durations, peak frequency, bandwidth, etc. The segmentation must thus be accurate and robust to reverberation.

Previous studies have done this either manually using spectrogram based methods [1,2], or used a peak-frequency (PF) based method [3-4], and have all been lab based. The peak-frequency method involves finding the peak-frequency of the call, and low/high-pass filtering the call at X % (where X is typically 97-99%) of peak-frequency. There are no shared code implementations for the PF methods. I'm also not sure if peak-frequency methods work in noisy, off-axis recorded calls.

Do any of you know of, perhaps alternate, openly available implementations of CF-FM segmentation methods?

References

1. Vater, M, M Kossl, E Foeller, F Coro, E Mora, and IJ Russell. 2003. “Development of Echolocation Calls in the Mustached Bat, Pteronotus Parnellii.” Journal of Neurophysiology 90 (4): 2274–90.
2. Fawcett, Kayleigh, David S Jacobs, Annemarie Surlykke, and John M Ratcliffe. 2015. “Echolocation in the Bat, Rhinolophus Capensis: The Influence of Clutter, Conspecifics and Prey on Call Design and Intensity.” Biology Open 4 (6): 693–701
3. Schoeppler, Diana, Hans-Ulrich Schnitzler, and Annette Denzinger. 2018. “Precise Doppler Shift Compensation in the Hipposiderid Bat, Hipposideros Armiger.” Scientific Reports 8 (1): 1–11.
4. Lu, Manman, Guimin Zhang, and Jinhong Luo. 2020. “Echolocating Bats Exhibit Differential Amplitude Compensation for Noise Interference at a Sub-Call Level.” Journal of Experimental Biology 223 (19)

Answer 1

There is one tool, the itsfm package that I wrote. While I'm not sure if it's the fastest tools to use, it is one of the open-source tools available to segment sounds into their CF and FM components.

The Pseudo-Wigner-Ville-Distribution method (pwvd in the package) generates a high-resolution time-frequency representation and tracks the dominant frequency over time. The modulation of the dominant frequency is also calculated, and used to segment sounds into CF and FM components.

In terms of accuracy and robustness, see the accompanying preprint for a performance comparison of the peak-percentage and PWVD methods.