Editing Chirplet transform

[[Image:Wave-chirp-wavelet-chirplet-en.svg|thumb|244px|Comparison of [[wave]], [[wavelet]], [[chirp]], and [[chirplet]]<ref>From page 2749 of "The Chirplet Transform: Physical Considerations", S. Mann and S. Haykin, IEEE Transactions on Signal Processing, Volume 43, Number 11, November 1995, pp. 2745–2761.</ref> ]]
[[Image: Pete with deltyburn abakography robot chirplet c.jpg|thumb|244px|Chirplet in a [[computer-mediated reality]] environment.]]
In [[signal processing]], the '''chirplet transform''' is an [[inner product]] of an input signal with a family of analysis primitives called '''chirplets'''.<ref name=mann>S. Mann and S. Haykin, "[http://wearcam.org/chirplet/vi91/index.htm The Chirplet transform: A generalization of Gabor's logon transform]", ''Proc. Vision Interface 1991'', 205&ndash;212 (3&ndash;7 June 1991).</ref><ref name="miho">D. Mihovilovic and R. N. Bracewell, "Adaptive chirplet representation of signals in the time–frequency plane," ''Electronics Letters'' '''27''' (13), 1159&ndash;1161 (20 June 1991).</ref>

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 (inventor)|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:

{{blockquote|A wavelet is a piece of a wave, and a chirplet, similarly, is a piece of a chirp. More precisely, a chirplet is a windowed portion of a chirp function, where the window provides some time localization property.  In terms of time–frequency space, chirplets exist as rotated, sheared, or other structures that move from the traditional parallelism with the time and frequency axes that are typical for waves (Fourier and [[short-time Fourier transform]]s) or [[wavelet]]s.}}

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.<ref name=mann/> In that paper,<ref name=mann/> 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 [[Ronald N. Bracewell|Bracewell]] later that same year.<ref name="miho"/>

==Applications==
[[Image:P-type-chirplets-for-image-processing.png|thumb|245px|(a) In image processing, periodicity is often subject to projective geometry (i.e. chirping that arises from projection). (b) In this image, repeating structures like the alternating dark space inside the windows, and light space of the white concrete, ''chirp'' (increase in frequency) towards the right. (c) The chirplet transform is able to represent this modulated variation compactly.]]

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).<ref>Mann, Steve, and Simon Haykin. "The chirplet transform: A generalization of Gabor’s logon transform." Vision interface. Vol. 91. 1991.</ref><ref>WaterHCI Part 1: Open Water Monitoring
with Realtime Augmented Reality, IEEE SPICES, INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING, INFORMATICS, COMMUNICATION AND ENERGY SYSTEMS 2022
(IEEE SPICES 2022), 10 - 12 MARCH, 2022, Nalanchira, Trivandrum, Kerala, India, 6 pages</ref>

Other applications of the chirplet transform in WaterHCI include the SWIM (Sequential Wave Imprinting Machine).<ref name="Mann, Steve 1992">Mann, Steve. "Time-Frequency" Perspectives”." Advances in Machine Vision: Strategies and Applications 32 (1992): 99.</ref><ref>Mann, Steve, et al. "Water-Human-Computer-Interface (WaterHCI): Crossing the Borders of Computation, Clothes, Skin, and Surface."</ref>

More recently other practical applications have been developed, including image processing (e.g. where there is periodic structure imaged through projective geometry),<ref name="Mann, Steve 1992"/><ref>Mann, Steve, and Simon Haykin. "Adaptive." Optical Engineering 31.6 (1992): 1243-1256.</ref>
as well as to excise chirp-like interference in spread spectrum communications,<ref>{{cite conference |mode=cs2 | last1 = Bultan
 | first1 = A.
 | date = May 1998
|book-title=Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
 | volume = 6
 | issue =4
 | pages =3265–3268
 | doi =10.1109/ICASSP.1998.679561
|title=A novel time-frequency exciser in spread spectrum communications for chirp-like interference
 | last2 = Akansu
 | first2 = A.N.
 | isbn = 0-7803-4428-6
 }}</ref> in EEG processing,<ref>{{Citation
 |last1        = Cui
 |first1       = J.
 |date         = 17 February 2005
 |title        = Time–frequency analysis of visual evoked potentials using chirplet transform
 |periodical   = Electronics Letters
 |volume       = 41
 |issue        = 4
 |pages        = 217–218
 |url          = http://www.eyetap.org/papers/docs/CuiTime_frequency_chirplet_vep.pdf
 |doi          = 10.1049/el:20056712
 |accessdate   = 2010-07-29
 |last2        = Wong
 |first2       = W.
 |last3        = Mann
 |first3       = S.
 |bibcode      = 2005ElL....41..217C
 |archive-date = 2011-07-16
 |archive-url  = https://web.archive.org/web/20110716055615/http://www.eyetap.org/papers/docs/CuiTime_frequency_chirplet_vep.pdf
 |url-status   = dead
}}</ref> and Chirplet Time Domain Reflectometry.<ref>{{Cite web | url=http://zone.ni.com/devzone/cda/epd/p/id/5684 | title=Example Programs - National Instruments | access-date=2007-12-31 | archive-url=https://web.archive.org/web/20120214211037/http://zone.ni.com/devzone/cda/epd/p/id/5684 | archive-date=2012-02-14 | url-status=dead }}</ref>

==Extensions==
The warblet transform<ref>Mann, Steve, and Simon Haykin. "[http://wearcam.org/chirplets_and_warblets.pdf 'Chirplets' and'warblets': novel time-frequency methods.]" Electronics letters 28, no. 2 (1992): 114-116.</ref><ref>
Mann, S., & Haykin, S. (1992, March). Time-frequency perspectives: the chirplet transform. In Acoustics, Speech, and Signal Processing, 1992. ICASSP-92., 1992 IEEE International Conference on (Vol. 3, pp. 417-420). IEEE.</ref><ref>
Angrisani, L., D'Arco, M., Moriello, R. S. L., & Vadursi, M. (2005). On the use of the warblet transform for instantaneous frequency estimation. Instrumentation and Measurement, IEEE Transactions on, 54(4), 1374-1380.</ref><ref>
Angrisani, L., Arco, M. D., Moriello, R. S. L., & Vadursi, M. (2004, August). Warblet transform based method for instantaneous frequency measurement on multicomponent signals. In Frequency Control Symposium and Exposition, 2004. Proceedings of the 2004 IEEE International (pp. 500-508). IEEE.</ref><ref>
Kazemi, S., Ghorbani, A., Amindavar, H., & Morgan, D. R. (2016). Vital-Sign Extraction Using Bootstrap-Based Generalized Warblet Transform in Heart and Respiration Monitoring Radar System.</ref><ref>
Zelinsky, N. R., & Kleimenova, N. G. Chirplet transform as the useful tool for study the time-frequency structure of geomagnetic pulsations.</ref> 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==
* [[Time–frequency representation]]
* Other time–frequency transforms
** [[Fractional Fourier transform]]
** [[Short-time Fourier transform]]
** [[Wavelet transform]]

==References==
{{Reflist}}
* {{citation
|first1=S.
|last1= Mann
|first2= S.
|last2= Haykin
|editor-first1= Simon
|editor-last1= Haykin
|chapter=Adaptive chirplet: An adaptive generalized wavelet-like transform
|url=http://wearcam.org/chirplet/adaptive_chirplet1991/
|title=Adaptive Signal Processing
|doi=10.1117/12.49794
|volume=1565
|pages= 402–413
|date= 21–26 July 1991|s2cid= 9418542
}} LEM, Logon Expectation Maximization
* {{cite journal
|first1=S.
|last1= Mann
|first2=S.
|last2=Haykin
|url=http://wearcam.org/chirplet/adaptive_chirplet1992/
|title= Adaptive chirplet transform
|journal=Optical Engineering
|volume=31
|issue=6
|pages=1243–1256
|doi=10.1117/12.57676
|bibcode=1992OptEn..31.1243M
|year=1992}} introduces Logon Expectation Maximization (LEM) and Radial Basis Functions (RBF) in Time–Frequency space.
* Osaka Kyoiku, [http://www.osaka-kyoiku.ac.jp/~ashino/pdf/2528.pdf Gabor, wavelet and chirplet transforms...(PDF)]
* J. "Richard" Cui, etal, [http://www.eyetap.org/papers/docs/CuiTime_frequency_chirplet_vep.pdf Time–frequency analysis of visual evoked potentials using chirplet transform] {{Webarchive|url=https://web.archive.org/web/20110716055615/http://www.eyetap.org/papers/docs/CuiTime_frequency_chirplet_vep.pdf |date=2011-07-16 }}, IEE Electronics Letters, vol. 41, no. 4, pp.&nbsp;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.

==External links==
* [http://tfd.sourceforge.net/ DiscreteTFDs - software for computing chirplet decompositions and time–frequency distributions]
* [http://wearcam.org/chirplet.htm The Chirplet Transform] (web tutorial and info).

[[Category:Transforms]]
[[Category:Fourier analysis]]
[[Category:Time–frequency analysis]]
[[Category:Image processing]]
[[Category:Radar signal processing]]