Phase-Based Tracking Carries Instantaneous-Frequency Analysis of Animal Calls While Synchrosqueezing Remains Untested There

Question: How have time-frequency reassignment and synchrosqueezing methods been used to extract instantaneous frequency trajectories from nonstationary animal vocalizations, and how do they compare with phase-based tracking?

Answer

Across the retrieved literature, the comparison the question presupposes has not been made: no study in this corpus applies reassignment or synchrosqueezing to animal vocalizations, so there is no empirical head-to-head with phase-based tracking. What does exist is a single explicit trajectory framework — phase-based frequency tracking that represents amplitude as a function of instantaneous frequency — demonstrated on 801 calls from 15 species of Saxicola [2]. The indirect evidence that bears on the comparison is consistent and points one way: windowed spectral representations impose a resolution trade-off that is large enough to change downstream model behaviour [13] [12], amplitude variation biases conventional instantaneous-frequency estimators unless envelope-curvature terms are corrected [14], and fixed-window frequency estimation systematically smooths away transient modulation that cycle-resolved estimation recovers, at a stated precision cost [10]. Taken together, these papers support phase-resolved or phase-free analytic estimators as the better-motivated default for rapidly modulated vocalizations, while leaving entirely open whether time-frequency reassignment or synchrosqueezing would improve trajectory fidelity if anyone actually ran it on call data.

Phase-based tracking is the only trajectory method demonstrated on real vocalization corpora

The one retrieved implementation justifies itself on exactly the problem that motivates reassignment methods: quantitative characterisation of call structure is described as challenging when frequency and amplitude vary jointly over time, and the proposed answer is a phase-based frequency tracker representing amplitude as a function of instantaneous frequency, from which features describing the frequency trajectory and temporal structure of individual calls are extracted [2]. That method was applied at corpus scale — 801 calls, 49 recordings, 15 species — and the resulting feature matrix was summarised with PCA and robust PCA, with robust PCA concentrating the variance of the low-rank representation into fewer components than conventional PCA [2]. The same study is explicit that uneven species representation and uncertainty in individual identity and taxonomic labels limit the biological conclusions [2].

The biological motivation for trajectory-level rather than parameter-level description is visible elsewhere: elephant rumbles show significant within-call spectral variation and complex patterns of frequency modulation, contradicting their treatment as homogeneous acoustic units [1]. By contrast, much comparative work still reduces calls to scalar descriptors — duration, minimum, maximum and centre frequency, bandwidth — with duration negatively correlated with maximum and centre frequency in Bryde's whale signals [8]. Scalar summaries and trajectory tracking answer different questions, and only the latter is at issue here.

Windowed time-frequency resolution is a consequential, non-neutral choice for call analysis

Spectrogram-based pipelines are described as limited by the uncertainty principle, which forces a trade-off between time and frequency resolution, with wavelet transforms offered as an alternative that gives better time resolution at high frequencies [13]. That trade-off is not a background nuisance but a parameter with measurable downstream consequences: an FFT window length sweep on bottlenose dolphin whistle detection found that N_fft = 256 significantly outperformed 512, 1024 and 2048 in cross-domain macro F1 while holding false discovery rate at zero across folds and thresholds, whereas N_fft = 128 matched recall but produced non-zero FDR in all folds — a transfer failure invisible to in-domain validation [12]. The authors frame this explicitly as a test of the assumption that window length is a neutral preprocessing detail, and report that it is not [12].

Where the frequency structure of interest is fine relative to the carrier, analysts respond by analysing the same recordings at two resolutions: orca vocalizations were examined with both narrowband and broadband spectrograms, revealing formant patterns and diphthongal trajectories argued to be independent of fundamental frequency and high-frequency content [11]. Comparative work also encodes frequency modulation as a score relative to trade-off boundaries — voiced and unvoiced modulation scores derived from vocal deviation — rather than as a tracked trajectory [5].

Amplitude–frequency co-variation is the specific bias that phase-free instantaneous-frequency estimators target

A complex Teager–Kaiser energy operator estimator is presented as making envelope-curvature terms explicit, thereby correcting a bias that affects conventional estimators and giving an accurate local frequency estimate in conditions where magnitude variations contribute non-negligibly to signal dynamics, without phase unwrapping [14]. That is precisely the regime the Saxicola tracker names as its target [2], and the two approaches are complementary rather than redundant: one is phase-based, the other deliberately avoids phase unwrapping.

Direct evidence on the cost of windowed estimation comes from an analogous rhythmic-tracking problem: frequency estimation over a fixed 0.5 s Fourier window failed to capture transient variability, while a cycle-by-cycle peak-and-trough method recovered higher, time-resolved frequencies and revealed cycle-level variability — at the acknowledged expense of precision in frequency estimation [10]. Model-based AM-FM decomposition shows the same window dependence in audio: an adaptive quasi-harmonic model estimated by least squares outperformed a subspace-based damped-sinusoid model at medium-to-large window sizes on highly nonstationary signals including singing voice, while the subspace method was better for small windows [7].

Synchrosqueezing appears in the retrieved literature only for non-vocal biosignals and has no phase-tracking comparator

The sole synchrosqueezing application retrieved is extraction of breathing dynamics from single-lead ECG, where the transform is combined with an ECG-derived-respiration algorithm to handle highly irregular heart rates in atrial fibrillation, and is reported as the first algorithm able to recover breathing dynamics in that population from a single lead [6]. This establishes synchrosqueezing as a tool for recovering instantaneous dynamics from nonstationary biological signals, but the paper reports no comparison against phase-based or analytic-signal tracking and uses no vocalization data [6]. No retrieved paper applies reassignment to animal calls at all. The comparison the question asks for is therefore an inference from adjacent domains, not a reported result.

For broadband transients, parametric modal models displace trajectory extraction entirely

Where calls are short broadband transients, the stated problem is that their internal oscillatory structure is difficult to compare in a sequence using conventional time- or frequency-domain representations, and the proposed solution is a sparse superposition of delayed damped resonant modes estimated by Burg autoregressive pole estimation, sparse approximation over an over-complete dictionary, and nonlinear parameter refinement [9]. Evaluated on free-ranging common dolphin recordings, this representation separated resonant behaviour from temporal localisation and produced repeatable parameters robust to wave, vessel and sonar interference [9]. This is a genuine competitor to ridge tracking for click-like signals: it abandons the single-valued frequency trajectory rather than trying to sharpen it.

Conflicts and gaps

The literature retrieved here does not contain a single experiment comparing synchrosqueezing, reassignment and phase-based tracking on the same vocalization dataset, so the relative accuracy of the three is unknown rather than merely uncertain. The only phase-based vocalization tracker is a single-author preprint whose own stated limits are taxonomic sampling and label uncertainty [2]; no retrieved paper reports trajectory error against a synthetic signal with a known modulation law. Two retrieved findings pull in opposite directions on the practical question of window choice: short windows are argued to be necessary to capture transient modulation [10], while a cross-domain whistle detector performed best at an intermediate window and degraded at both extremes [12], and the AM-FM model comparison shows the better estimator depends on window size [7]. How any of these methods behaves on multi-harmonic or overlapping calls is not addressed in the retrieved abstracts, and the Saxicola method's representation of amplitude as a function of instantaneous frequency is not described there in terms of multi-component handling [2].

What would change the answer

A benchmark with known ground truth would settle it: synthesise calls under controlled frequency-modulation laws, inject noise at measured SNR, and score reassignment, synchrosqueezing, complex-Teager–Kaiser estimation [14], cycle-resolved estimation [10] and phase-based tracking [2] on trajectory RMSE and modulation-depth fidelity. Physiologically grounded targets are available rather than merely synthetic ones: zebra finch heat calls are described as extremely soft frequency-modulated calls with dominant frequencies of 6.8 ± 0.6 kHz [3], and a pipeline recovering subsyringeal pressure and syringeal tension from the waveform — validated against recorded air sac pressure across 44 songs from twelve birds — supplies a motor-coordinate reference against which acoustic trajectory estimates can be checked [4], with direct respiratory pressure recordings during song providing a further independent signal [15]. Re-running the dolphin whistle window-length protocol [12] with instantaneous-frequency error as the criterion instead of detection F1 would convert a detection-tuning result into a trajectory-estimation result, and applying the sparse modal representation [9] as a baseline on the same tonal calls would test whether ridge-finding is the right framing at all.

References

[1] Rantsiou, E.. "Elephant rumble vocalizations: spectral substructures and superstructures". bioRxiv. 2025-08-09T00:00:00.000Z. URL: https://doi.org/10.1101/2024.03.10.584305

[2] Strijbos, F.. "Phase-Based Frequency Tracking and Analysis of Vocalisations in the Genus Saxicola". bioRxiv. 2026-10-19T00:00:00.000Z. URL: https://doi.org/10.64898/2026.10.14.759137

[3] Anttonen, T., Loning, H., Felbo, F. M., Christensen-Dalsgaard, J., Griffith, S. C., Naguib, M., Elemans, C. P.. "Zebra finches produce intralaryngeal laminar flow whistles during panting". bioRxiv. 2025-02-14T00:00:00.000Z. URL: https://doi.org/10.1101/2025.02.14.638254

[4] Ostrowski, L. M., Mendez, J. M., Tostado-Marcos, P., Cooper, B. G., Gentner, T. Q.. "Automated inference of respiratory and syringeal biomechanical trajectories from birdsong acoustics". bioRxiv. 2026-08-04T00:00:00.000Z. URL: https://doi.org/10.64898/2026.08.03.742634

[5] Sierro, J., de Kort, S. R., Zollinger, S. A., Hartley, I. R.. "A new fitness indicator in birdsong: a trade-off between song length and note length". bioRxiv. 2026-10-15T00:00:00.000Z. URL: https://doi.org/10.64898/2025.12.05.692489

[6] Wu Hau-Tieng, Chan Yi-Hsin, Lin Yu-Ting, Yeh Yung-Hsin. "Using synchrosqueezing transform to discover breathing dynamics from ECG signals". arxiv. 2026-06-03T00:00:00.000Z. URL: https://arxiv.org/abs/1105.1571

[7] George P. Kafentzis. "On the Parameter Estimation of Sinusoidal Models for Speech and Audio Signals". arxiv. 2026-03-04T00:00:00.000Z. URL: https://arxiv.org/abs/2401.01255

[8] Yang, Y., Li, X., Li, M., Zhang, Y., Chen, M., Fan, F., Wang, K., Du, H.. "Acoustic Characteristics of Low-Frequency Vocalizations of Bryde's Whales (Balaenoptera edeni edeni) in the Weizhou Island Waters of the Beibu Gulf, China". bioRxiv. 2026-06-23T00:00:00.000Z. URL: https://doi.org/10.64898/2026.06.17.729802

[9] Strijbos, F.. "A Sparse Modal Representation for Dolphin Echolocation Transients". bioRxiv. 2026-10-19T00:00:00.000Z. URL: https://doi.org/10.64898/2026.10.14.759144

[10] Guanghui Li, Fangyuan Li, Barbara Lykke Lind, Rune W Berg. "Cycle Based Computational Pipeline for Extracting Instantaneous Whisking Frequency". arxiv. 2026-05-28T00:00:00.000Z. URL: https://arxiv.org/abs/2605.27573

[11] Begus, G., Holt, M., Wright, B., Gruber, D. F.. "Orca vowels and consonants: convergent spectral structures across cetacean and human speech". bioRxiv. 2026-03-02T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.27.708287

[12] De Marco, R., Iurcev, M., Trebbi, A., Lagorio, S.. "Is FFT window length a neutral preprocessing choice in CNN-based dolphin whistle detection? A cross-domain sensitivity analysis.". bioRxiv. 2026-09-08T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.01.721665

[13] Christopher Hauer. "Detection and Classification of Cetacean Echolocation Clicks using Image-based Object Detection Methods applied to Advanced Wavelet-based Transformations". arxiv. 2026-02-23T00:00:00.000Z. URL: https://arxiv.org/abs/2602.17749

[14] A. Vaca, J. Gutierrez Florensa, F. Milano. "Instantaneous Frequency in Power Systems using the Teager-Kaiser Energy Operator". arxiv. 2026-10-14T00:00:00.000Z. URL: https://arxiv.org/abs/2601.15099

[15] Kizhakoot, D. B., Kalra, S., PR, R., Chorol, S., Chitnis, S., Rao, D., Rajan, R.. "Respiratory vocal coordination increases as zebra finches prepare to sing". bioRxiv. 2025-05-15T00:00:00.000Z. URL: https://doi.org/10.1101/2025.05.14.654126

How this survey was made

This survey answers one question: “How have time-frequency reassignment and synchrosqueezing methods been used to extract instantaneous frequency trajectories from nonstationary animal vocalizations, and how do they compare with phase-based tracking?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 15 papers whose work this text draws on, chosen from the 122 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 22, 2026 and covered work from the previous two years.