  This work revisits a class of biomimetically inspired log-periodic waveforms
first introduced by R.A. Altes in the 1970s for generalized target description.
It was later observed that there is a close connection between such sonar
techniques and wavelet decomposition for multiresolution analysis. Motivated by
this, we formalize the original Altes waveforms as a family of hyperbolic
chirplets suitable for the detection of accelerating time-series oscillations.
The formalism results in a remarkably flexible set of wavelets with desirable
properties of admissibility, regularity, vanishing moments, and time-frequency
localization. These "Altes wavelets" also facilitate efficient implementation
of the scale invariant hyperbolic chirplet transform (HCT).
  From a practical perspective, log-periodic oscillations with an acceleration
towards criticality can serve as indicators of an incipient bifurcation. Such
signals abound in nature, often as precursors to phase transitions in the
non-linear dynamics of complex systems. For example, the authors' interest lies
in automatic detection of the well documented phenomenon of log-periodic price
dynamics during financial bubbles and preceding market crashes. However, the
methodology presented here is more widely applicable in such diverse domains as
prediction of critical failures in mechanical systems, and fault detection in
electrical networks. Examples beyond failure diagnostics include animal species
identification via call recordings, commercial \& military radar, and there are
many more. A synthetic application is presented in this report for illustrative
purposes.
