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This work revisits a class of biomimetically inspired log-periodic waveformsfirst introduced by R.A. Altes in the 1970s for generalized target description.It was later observed that there is a close connection between such sonartechniques and wavelet decomposition for multiresolution analysis. Motivated bythis, we formalize the original Altes waveforms as a family of hyperbolicchirplets suitable for the detection of accelerating time-series oscillations.The formalism results in a remarkably flexible set of wavelets with desirableproperties of admissibility, regularity, vanishing moments, and time-frequencylocalization. These "Altes wavelets" also facilitate efficient implementationof the scale invariant hyperbolic chirplet transform (HCT).  From a practical perspective, log-periodic oscillations with an accelerationtowards criticality can serve as indicators of an incipient bifurcation. Suchsignals abound in nature, often as precursors to phase transitions in thenon-linear dynamics of complex systems. For example, the authors' interest liesin automatic detection of the well documented phenomenon of log-periodic pricedynamics during financial bubbles and preceding market crashes. However, themethodology presented here is more widely applicable in such diverse domains asprediction of critical failures in mechanical systems, and fault detection inelectrical networks. Examples beyond failure diagnostics include animal speciesidentification via call recordings, commercial \& military radar, and there aremany more. A synthetic application is presented in this report for illustrativepurposes.

The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform