Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars
Abstract
Hyperbolic Frequency-Modulated (HFM) signals possess optimal Doppler tolerance, making them a central point in bioacoustic echolocation research. While the Doppler invariance of HFM signals is a known property, the explicit analytical calculation of their Wideband Ambiguity Function (WAF) is required. In this paper, we provide the exact mathematical derivations of the WAF for both the finite rectangular envelope and the pure hyperbolic signal. Furthermore, we introduce the HYPerbolicity Index (HYPI) to quantify time-frequency hyperbolicity across four different Time-Frequency Representations (TFRs). We establish that the Reassigned Spectrogram Representation is the least prone to HFM misidentification. Moreover, by evaluating the HYPI on foraging sequences of a bat species (Pipistrellus kuhlii). We demonstrate that the Hyperlocalized Wavelet Transform (HLT) offers the most consistent modulation extraction.
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BibTeX
@misc{gac2026wideband,
title = {{Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars}},
author = {Baudouin Le Gac and Nicolas Deloustal and Hervé Glotin},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05801151v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars
AU - Baudouin Le Gac
AU - Nicolas Deloustal
AU - Hervé Glotin
PY - 2026
DA - 2026/10/16
PB - HAL
UR - https://hal.science/hal-05801151v2
AB - Hyperbolic Frequency-Modulated (HFM) signals possess optimal Doppler tolerance, making them a central point in bioacoustic echolocation research. While the Doppler invariance of HFM signals is a known property, the explicit analytical calculation of their Wideband Ambiguity Function (WAF) is required. In this paper, we provide the exact mathematical derivations of the WAF for both the finite rectangular envelope and the pure hyperbolic signal. Furthermore, we introduce the HYPerbolicity Index (HYPI) to quantify time-frequency hyperbolicity across four different Time-Frequency Representations (TFRs). We establish that the Reassigned Spectrogram Representation is the least prone to HFM misidentification. Moreover, by evaluating the HYPI on foraging sequences of a bat species (Pipistrellus kuhlii). We demonstrate that the Hyperlocalized Wavelet Transform (HLT) offers the most consistent modulation extraction.
ER -