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Topic: Chirplet

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	Otoacoustic Emissions Portal: Definitions CH-TEOAE
		Otherwise the chirplet stimuli may need to be adapted to compensate for the frequency response of the sound source.
		The chirplet signals should not be longer than 3 ms to allow a separation of stimulus and ear response.
		The basic idea to generate a chirplet signal for a given power spectrum is that the spectral energy at a certain frequency increases if the instantaneous frequency of the chirplet takes values close to this frequency during a longer period of time.
	www.otoemissions.org /definitions/CH-TEOAE.html (1072 words)

	Chirplet transform - Wikipedia, the free encyclopedia
		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 transforms) or wavelets.
		The chirplet transform is a useful signal analysis and representation framework that is widely used in radar, biomedical signal processing, and image processing.
		Whereas the wavelet transform is based on wavelets of the form g(ax+b), the p-type chirplet transform is based on chirplets of the form g((ax+b)/cx+1), where a is the scale, b is the translation, and c is the chirpiness (chirp-rate, as defined by the degree of perspective, or projection).
	en.wikipedia.org /wiki/Chirplet (1044 words)

	Projects
		The chirplet transform subsumes both Fourier analysis and wavelet analysis (as well as several other classes of time-frequency analysis) as lower dimensional subspaces in the chirplet analysis space, providing a flexible framework for characterizing the full range of auditory cortical sensitivities observed in mammals.
		The chirplet transform retains the advantages offered by time-frequency and wavelet transforms, and additionally provides a natural way for characterizing the different types of processing that have been described for different auditory fields (cortical regions with systematically related response sensitivities).
		Chirplet spaces are highly overcomplete (redundant) because there are an infinite number of ways to segment a time-frequency plane.
	www.acsu.buffalo.edu /~emiii/projects.htm (1343 words)

	Chirplet transform explained (Site not responding. Last check: 2007-10-17)
		Comparison of [[wave, wavelet, chirp, and chirplet ]] In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.
		The term "chirplet" was reportedly coined by Steve Mann in the 1980s to describe a windowed portion of a chirp function.
		Loosely speaking, a wavelet is a piece of a wave, and similarly a chirplet is a piece of a chirp.
	www.wordspider.net /ch/chirplet-transform.html (1213 words)

	The Chirplet Transform: Physical Considerations - Mann, Haykin (ResearchIndex) (Site not responding. Last check: 2007-10-17)
		8, the objective function (3) being the cross chirplet transform.
		8 The chirplet transform --- a generalization of Gabor's logon..
		3 Adaptive chirplet representation of signals on time--frequen..
	citeseer.ist.psu.edu /20492.html (991 words)

	The Chirplet Transform
		Four examples of chirplets (note for example, that a wave is a special case of a chirplet where the "chirprate" is zero and the window size is infinity).
		The Gaussian chirplet transform in the above paper was inspired by Gabor's 1946 paper on communication.
		In an adaptive version of the chirplet tranform, a smaller number of chirplets are used to approximate an arbitrary signal, by selecting a small number of chirplets that, when added together, best describe the signal.
	wearcam.org /chirplet.htm (760 words)

	Wavelet Digest, Vol. 1, Nr. 6. (Site not responding. Last check: 2007-10-17)
		In short, a ``chirplet'' is a piece of a chirp, in the same sense that a wavelet is, loosely speaking, a piece of a wave.
		The chirplet, is the family of time-frequency-affinites: the family is generated from one mother chirplet by affine coordinate changes in the time-frequency plane.
		This generalization of the wavelet is different than the TF-affinities but the two generalizations are combined in the paper, and explanation is given as to when subgroup transforms of the former are more appropriate versus when the latter is the more appropriate.
	www.ucalgary.ca /~morrow/Wavelets/msg00006.html (1460 words)

	The Chirplet Transform: Physical Considerations
		In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear-in-time (obtained through convolution with a q-chirp) and shear-in-frequency (obtained through multiplication by a q-chirp).
		Signals in this multidimensional space can be obtained by a new transform which we call the ``q-chirplet transform'', or simply the ``chirplet transform''.
		The proposed chirplets are generalizations of wavelets, related to each other by two-dimensional affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets which are related to each other by one-dimensional affine coordinate transformations (translations and dilations) in the time-domain only.
	wearcam.org /chirplet/chirplet.html (311 words)

	EyeTap Personal Imaging Lab
		This property allows us to use it as an alternate means of computing the FF plane of the chirplet transform, by using the TF plane as our input image.
		The Radon transform provides us with a simple means of computing the FF plane of the autochirplet transform, by using the Wigner distribution, and arriving at a transform space that tells us basically the same information as the chirplet FF-plane, except that we benefit from the greater resolution of the Wigner distribution.
		It is easier to compare the Radon transform of the Wigner distribution with the chirplet CF plane (Fig.
	www.eyetap.org /wearcomp/chirplet/node21.html (592 words)

	chirplab.org
		The methods in ChirpLab might be especially suitable for the detection of gravitational waves in data from laser interferometric detectors such as LIGO.
		The methods are based on wave snippets called chirplets and network optimization algorithms that link together local empirical correlations into a coherent and meaningful event.
		The idea is to use structured algorithms which exploit information in the so-called chirplet graph to chain chirplets together adaptively as to form chirps with polygonal instantaneous frequency.
	www.chirplab.org (379 words)

	Chirplet considerations - Authors - C (Site not responding. Last check: 2007-10-17)
		Citations: Adaptive chirplet representation of signals on time--frequency plane - Mihovilovic, Bracewell (...
		Haykin: Adaptive 'chirplet' transform: an adaptive generalization of the wavelet transform: OE 31...
		He is also the inventor of the wristwatch videophone, of the chirplet transform (a new...
	homegarden4u.info /chirplet-considerations.htm (354 words)

	Atomic Decomposition of Whale Whistles
		Chirplets are Gaussians that are parameterized by their location in time, location in frequency, chirp rate, and duration.
		We proposed to do this by estimating the chirplet parameters with maximum likelihood estimation.
		It is number 14 from the NUWC data set and the dynamic range in the spectrogram is 50 dB.
	tfd.sourceforge.net /Whale (121 words)

	Chirplet transform - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-17)
		Mann and S. Haykin, "The Chirplet transform: A generalization of Gabor's logon transform (http://wearcam.org/chirplet/vi91/index.htm)", Proc.
		D. Mihovilovic and R. Bracewell, "Adaptive chirplet representation of signals in the time-frequency plane," Electronics Letters 27 (13), 1159–1161 (20 June 1991).
		Mann and S. Haykin, "The adaptive chirplet: An adaptive wavelet like transform (http://wearcam.org/chirplet/adaptive_chirplet1991/)", Proc.
	www.phatnav.com /wiki/index.php?title=Chirplet (1034 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		Abstract: This paper proposes efficient algorithms for approximating complex-valued and real-valued signals as a weighted sum of multiple chirplet atoms, which are characterized by four parameters, namely the scale, time, frequency and chirp rate.
		Direct sequential etimation of the parameters of the initial chirplets significantly affect the parameter estimation of the subsequent chirplets and may result in large chirplet approximation errors.
		Unlike previous methods, our chirplet approximations require neither any a priori complete dictionary of chirplets nor complicated multi-dimensional searches to obtain suitable choices of chirplet parameters.
	www.math.cmu.edu /~nw0z/public_html/publications/06-CNA-002/002abs/002abs.html (139 words)

	The pyramidal (multi-resolution) CCT (Site not responding. Last check: 2007-10-17)
		To compute the proposed hierarchical CCT, we repeat the computation of the CCT (14) for each of the desired tile sizes and place them in a six-dimensional space, equally spaced along the sixth coordinate axis.
		Various 2-D slices through the multiresolution CCT may correspond to useful tilings of the TF plane with true parallelograms (true to the extent that the DPSS define a truly rectangular region in the TF plane).
		It would therefore be possible to use these results to define more general parameterizable transforms, based on families of multiple analysis primitives acting collectively in the TF plane.
	crydee.sai.msu.su /~vab/Wavelet.rsc/Chirplet.dir/node16.html (281 words)

	Hewlett-Packard Journal: Wavelet analysis: theory and applications - Technical - Tutorial
		(30) [Mathematical Expression Omitted] where the [c.sub.k] are the chirplet basis functions, [f.sub.k] is the frequency Of [c.sub.k], a is a measure of the 'sharpness" of the chirplet, and r is a frequency drift rate parameter.
		26 and 27 represent the results of the conventional wavelet transform and the chirplet transform, respectively.
		The chirplet transform analysis, on the other hand, can separate the two components clearly.
	www.findarticles.com /p/articles/mi_m0HPJ/is_n6_v45/ai_16314517/pg_3 (847 words)

	The Chirplet Transform: Physical Considerations - Mann, Haykin (ResearchIndex) (Site not responding. Last check: 2007-10-17)
		8, the objective function (3) being the cross chirplet transform.
		6 The chirplet transform --- a generalization of Gabor's logon..
		3 Adaptive chirplet representation of signals on time--frequen..
	sherry.ifi.unizh.ch /55741.html (965 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		Baraniuk and D. Jones, Wigner-Based Formulation of the Chirplet Transform, IEEE Transactions on Signal Processing, (Submitted, December 1996).
		Using the Wigner distribution, we derive and analyze a matrix formulation for the chirplet transform, a signal analysis tool that generalizes the wavelet and short-time Fourier transforms.
		The formulation expresses the translations, scalings, and shears of the chirplet transform in terms of affine matrix transformations on the time-frequency plane.
	cmc.rice.edu /docs/docinfo.aspx?doc=Bar1996Dec1WignerBase (133 words)

	[No title]
		Furthermore, the chirplet transform is a framework for deriving new signal representations.
		The chirplet transform is a mapping from a 1-D domain to an 8-D range (in contrast to the wavelet, for example, which is a 1-D to 2-D mapping).
		The adaptive chirplet transform attempts to alleviate some of these problems by selecting an optimal set of bases without the need to manually intervene.
	www.spie.org /web/journals/oe/oe_jun92.html (4608 words)

	The Wavelet Digest :: View topic - Answer: Custom Designing Basis Functions
		Another method called "four parameter atomic decomposition" uses matching pursuits to decompose a signal into chirplets.
		Another chirplets decomposition method was suggested by Jeff O'Neil and Flandrin: it adaptively estimates the best chirplets instead of searching for them from an infinite dictionary.
		Bultan, A. (1999) A Four-Parameter Atomic Decomposition of Chirplets.
	www.wavelet.org /phpBB2/viewtopic.php?t=5299 (291 words)

	Title page for ETD etd-08242006-235147
		Due to the multi-modal and dispersive character of Lamb waves, displacement or energy related quantities can only be allocated to individual modes when they are separated in the time-frequency plane.
		The chirplet transform has been introduced as a generalization of both the wavelet and Short-time Fourier transform.
		It offers additional degrees of freedom to adjust time-frequency atoms which can be exploited in a model-based approach to match the group delay of individual modes.
	etd.gatech.edu /theses/available/etd-08242006-235147 (173 words)

	Research of D.L. Jones' group
		Contributed several advances in generalized joint signal representations, including a time-frequency-based derivation of the chirplet transform, new orthogonal chirped bases, and unitarily transformed joint signal representations.
		We showed the equivalence of Cohen's and Baraniuk's methods for constructing general joint signal representations and contributed new insights to this theory.
		Developed the chirplet transform from a time-frequency context.
	www.ifp.uiuc.edu /~jones/research.html (1456 words)

	Citations: The Adaptive Chirplet: An Adaptive Wavelet Like Transform - Mann, Haykin (ResearchIndex) (Site not responding. Last check: 2007-10-17)
		, 40] 41] 42] 43] 30] Comparisons between traditional TF methods and chirplets have also been made, in the context of practical applications in both radar [28] 44] and geophysics [30] Segal exploited various coordinate transformations in the TF plane in the development of his theory.
		Also, a logfrequency chirplet has been formulated where the underlying chirps appear as straight lines in the time scale plane.
		3 Overview This paper is devoted to physical (intuitive) considerations of the chirplet....
	citeseer.ist.psu.edu /context/203250/0 (311 words)

	Technical Session 2
		Taxonomies of the various search and track modes are reported, and an example radar resource configuration is described in detail.
		In this paper, we replace the Fourier transform by the adaptive Chirplet transform in the Doppler processing in OTHR when a target moves non-uniformly.
		The strength of our approach is verified by a series of simulation experiments based on a real phased array for air defense frigates.
	www.ewh.ieee.org /r6/lac/radar02/papers/session2.html (366 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		The authors apply a method of time-frequency analysis called chirplet analysis to study whistlers in the magnetosphere.
		They show that this procedure give better analysis results than the original method proposed by Gabor for the analysis of nonstationary wave phenomena.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=166724 (153 words)

	Radar - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-17)
		This shows that the received power declines as the fourth power of the range, which means that the reflected power from distant targets is very, very small.
		Other mathematical developments in radar signal processing include time-frequency analysis (Weyl Heisenberg or wavelet), as well as the chirplet transform which makes use of the fact that radar returns from moving targets typically "chirp" (change their frequency as a function of time, as does the sound of a bird or bat).
		In 1887 the German physicist Heinrich Hertz began experimenting with radio waves in his laboratory.
	encyclopedia.learnthis.info /r/ra/radar.html (5369 words)

	Moving target detection in over-the-horizon radar using adaptive chirplet transform
		When a target does not move uniformly, the Fourier-based techniques for the target detection including superresolution techniques may not work well.
		In this paper, we propose an adaptive chirplet transform technique in the Doppler processing in OTHR as an alternative of the Fourier transform technique when a target moves nonuniformly.
		Citation: Wang, G. Xia, B. Root, and V. Chen (2003), Moving target detection in over-the-horizon radar using adaptive chirplet transform, Radio Sci.
	www.agu.org /pubs/crossref/2003/2002RS002621.shtml (237 words)

	Wavelet Digital Signal Processing of Undersea Acoustic Data - Storming Media
		A Flexible Chirplet Transform algorithm has been developed.
		Building and implementation of chirplet reconstruction algorithms have been completed successfully.
		Feature extraction and noise removal for low frequency acoustic chirp signals have been completed using scalar wavelet, wavelet packet, multiwavelet, and chirplet and Fourier techniques.
	www.stormingmedia.us /47/4775/A477504.html (140 words)

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