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Chirplet transform

In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.

Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wavelet theory).

Definitions

The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself (apart from chirplet transform) was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words:

The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term chirplet (but not the term chirplet transform) was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year.

Applications

The first practical application of the chirplet transform was in water-human-computer interaction (WaterHCI) for marine safety, to assist vessels in navigating through ice-infested waters, using marine radar to detect growlers (small iceberg fragments too small to be visible on conventional radar, yet large enough to damage a vessel).

Other applications of the chirplet transform in WaterHCI include the SWIM (Sequential Wave Imprinting Machine).

More recently other practical applications have been developed, including image processing (e.g. where there is periodic structure imaged through projective geometry), as well as to excise chirp-like interference in spread spectrum communications, in EEG processing, and Chirplet Time Domain Reflectometry.

Extensions

The warblet transform is a particular example of the chirplet transform introduced by Mann and Haykin in 1992 and now widely used. It provides a signal representation based on cyclically varying frequency modulated signals (warbling signals).

See also

References

  • LEM, Logon Expectation Maximization
  • introduces Logon Expectation Maximization (LEM) and Radial Basis Functions (RBF) in Time–Frequency space.
  • Osaka Kyoiku, Gabor, wavelet and chirplet transforms...(PDF)
  • J. "Richard" Cui, etal, Time–frequency analysis of visual evoked potentials using chirplet transform , IEE Electronics Letters, vol. 41, no. 4, pp. 217–218, 2005.
  • Florian Bossmann, Jianwei Ma, Asymmetric chirplet transform—Part 2: phase, frequency, and chirp rate, Geophysics, 2016, 81 (6), V425-V439.
  • Florian Bossmann, Jianwei Ma, Asymmetric chirplet transform for sparse representation of seismic data, Geophysics, 2015, 80 (6), WD89-WD100.
  • L. Angrisani and M. D'Arco, "A measurement method based on a modified version of the chirplet transform for instantaneous frequency estimation," in IEEE Transactions on Instrumentation and Measurement, vol. 51, no. 4, pp. 704-711, Aug. 2002, doi: 10.1109/TIM.2002.803295.
  • Y. Lu, R. Demirli, G. Cardoso and J. Saniie, "A successive parameter estimation algorithm for chirplet signal decomposition," in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 53, no. 11, pp. 2121-2131, November 2006, doi: 10.1109/TUFFC.2006.152.
  • L. Sorenson, Y. Lu, F. Martinez-Vallina and J. Saniie, "Chirplet Transform Signal Decomposition for Echo Detection and Estimation," 2006 Fortieth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2006, pp. 509-512, doi: 10.1109/ACSSC.2006.354800.
  • Y. Yang, W. Zhang, Z. Peng and G. Meng, "Multicomponent Signal Analysis Based on Polynomial Chirplet Transform," in IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3948-3956, Sept. 2013, doi: 10.1109/TIE.2012.2206331.
  • Y. Yang, Z. K. Peng, G. Meng and W. M. Zhang, "Spline-Kernelled Chirplet Transform for the Analysis of Signals With Time-Varying Frequency and Its Application," in IEEE Transactions on Industrial Electronics, vol. 59, no. 3, pp. 1612-1621, March 2012, doi: 10.1109/TIE.2011.2163376.
  • A. Bhargava and S. Mann, "Adaptive Chirplet Transform-Based Machine Learning for P300 Brainwave Classification," 2020 IEEE-EMBS Conference on Biomedical Engineering and Sciences (IECBES), Langkawi Island, Malaysia, 2021, pp. 62-67, doi: 10.1109/IECBES48179.2021.9398775.
  • S. Mann, N. Kumar, J. P. Bicalho, M. Sibai and C. Leaver-Preyra, "Adaptive Chirplet Transform-Based Sleep State Detection," 2025 IEEE International Conference on Consumer Electronics (ICCE), Las Vegas, NV, USA, 2025, pp. 1-6, doi: 10.1109/ICCE63647.2025.10929845.
  • Y. Jiang, W. Chen, M. Li, T. Zhang and Y. You, "Synchroextracting chirplet transform-based epileptic seizures detection using EEG," in Biomedical Signal Processing and Control, vol 68, July 2021, doi: 10.1016/j.bspc.2021.102699

External links