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Topic: Chirplet transform

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	List of Fourier-related transforms - Wikipedia, the free encyclopedia
		Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum.
		Discrete-time Fourier transform (DTFT), the Fourier transform of a discrete sequence or, equivalently, the continuous Fourier Transform of continuous-time function consisting of a sequence of impulses.
		Discrete Fourier transform (DFT), the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies).
	en.wikipedia.org /wiki/List_of_Fourier-related_transforms (315 words)

	Chirplet transform - Article from FactBug.org - the fast Wikipedia mirror site (Site not responding. Last check: 2007-08-12)
		The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time-frequency plane.
		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).
	www.factbug.org /cgi-bin/a.cgi?a=1034358 (990 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)

	Wavelet - ExampleProblems.com
		Wavelets, wavelet analysis, and the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform (known as the mother wavelet).
		All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis.
		The wavelet transform is often compared with the Fourier transform, in which signals are represented as a sum of sinusoids.
	www.exampleproblems.com /wiki/index.php/Wavelet (1014 words)

	Fourier transform Information - fast fourier transform
		The circular aperture fourier transform rayleigh criterion transforms are linear operators and, with proper normalization, are unitary as well (a property known as Parseval's theorem or, more generally, as the Plancherel theorem, and most generally via Pontryagin duality).
		The transforms are invertible, and in fact the inverse transform has almost the same form as the forward transform.
		In terms of signal processing, the transform takes a time series representation fourier transform properties sheet of a signal function and short time fourier transform maps it into a frequency spectrum, where ω is angular frequency.
	www.inanot.com /Ina-Electronics_Topics_Em_-_F-/Fourier_transform.html (1190 words)

	[No title]
		It is shown that the wavelet transform appears to be a natural alternative to the decompositions commonly used in fluid dynamics and turbulence (i.e.
		Chirplets are generalized wavelets, related to eachother by two-dimensional affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, related to each other by one-dimensional affine coordinate transformations in the time-domain only (translations and dilations).
		The wavelet transform of the acceleration process of the transient flexural vibrations of an impact excited uniform beam resulted in a time-scale representation which provided a clear exposition of the time evolution of the spectral components during the dispersion process.
	ei.cs.vt.edu /~mm/cache/wavelet.txt (5815 words)

	Time-frequency perspectives: the 'chirplet' transform (Site not responding. Last check: 2007-08-12)
		Chirplet filters embody both the wavelet and STFT as special cases by decoupling the filter bandwidths and center frequencies.
		Chirplets, by their embodiment of affine geometry in the time-frequency (TF) plane, may also include shears in time and frequency (chirps) and even time-bandwidth product variation (noise bursts) if desired.
		The most general chirplets may be derived from one or more basic ('mother') chirplets by the transformations or perspective geometry in the TF plane.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/icassp/&toc=comp/proceedings/icassp/1992/0532/03/0532toc.xml&DOI=10.1109/ICASSP.1992.226187 (190 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)

	The Chirplet Transform: Physical Considerations
		The parameter space contains a ``time-frequency-scale volume'', and thus encompasses both the short-time Fourier transform (as a slice along the time and frequency axes), and the wavelet transform (as a slice along the time and scale axes).
		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)

	Historical Notes (Site not responding. Last check: 2007-08-12)
		In 1989 and early 1990, we formulated the chirplet transform, a multidimensional parameter space whose coordinate axes correspond to the pure parameters of planar affine coordinate transformations in the time-frequency plane.
		Later, we applied the chirplet transform and some of the new two-dimensional subspace transforms to problems in marine radar and obtained results that were better than previous methods, so we published these findingsmannVI91.
		In particular, time-shear and frequency-shear are examples of affine coordinate transformations - mappings from the TF-plane to the TF-plane - while the chirplet transform is a mapping from a continuous function of one real variable to a continuous function of five (or six) real variables.
	proxy.searchbuffer.com /go.html?key=5b5be08e6e2220db921c0f7670a7fbbe&base=http%3A%2F%2Fgenesis%2Eeecg%2Etoronto%2Eedu%2Fchirplet%2Fnode2%2Ehtml&url=http%3A%2F%2Fc%2Eenhance%2Ecom%2Fc%3Fe1%3DC5ssbxtD3OhdgYhgVFbGkuMbvIMsrqONCurRM1fxCJboHMP42bAerpqgkq3AjANOwqIzpMwCBYNV0mXtWPfuEqfHyOMTFBa1Al040uqukcKrtxzJWUlGB4FjxubGGXxfcEIBOnQhNDYA0pTGN3PvSznwydcn0mrhg3ICo5d3vdLNDgPn44UypwsnuSM2mmL1HRz3ZTk3An0rBARlKNJNNeTXVNaI5vLCJ1hxTgs1klZDVVEaH%26h%3Du5BU5l5zkhK2nCALS (765 words)

	SPIE Proceedings Vol. 4738
		We applied the Daubechies 1 wavelet transform to the x signal, y signal and pressure signal using the coefficients as inputs to a multi-layer perceptron trained with back-propagation on the sentence data.
		The peak of the local Radon transform is used as a measure for the velocity towards the radar of a moving target.
		The Radon transform of the cross-range time-frequency representation of the signal is used for focusing an ISAR image that has been blurred due to non-uniform target rotation.
	www.spie.org /web/abstracts/4700/4738.html (9403 words)

	What is Fractional Fourier transform (Site not responding. Last check: 2007-08-12)
		The fractional Fourier transform (FRFT) is a linear transformation generalizing the continuous Fourier transform, and it can be thought of as the Fourier transform to the n-th power where n need not be an integer — thus, it can transform a function to an intermediate domain between time and frequency.
		An early definition of the FRFT was given by Namias (1980), but it was not widely recognized until it was independently reinvented around 1993 by several groups of researchers (Almeida, 1994).
		See also the chirplet transform for a related generalization of the Fourier transform.
	www.whatis.tv /Fractional_Fourier_transform.html (358 words)

	[No title]
		We apply this new transform to a practical problem in marine radar: the detection of floating objects by their "acceleration signature" (the "chirpyness" of their radar backscatter), and obtain results far better than those previously obtained by other current Doppler radar methods.
		The fact that the chirplet transform of a chirplet itself is not a perfectly sharp spike is a consequence of the overlap of the bases and the fundamental resolution limit inherent in any transform.
		Figure 6 shows the chirplet transform of a signal which is itself a special case of a chirplet, namely a pure tone (modulating a Ganssian envelope).
	www.n1nlf-1.eecg.toronto.edu /chirplet/vi91/index.htm (4399 words)

	Definition of Chirplet
		Loosely speaking, a wavelet is a piece of a wave, and similarly a chirplet is a piece of a chirp.
		The term was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell in the same year.
		q-chirplets (quadratic chirplets) of the form exp(i 2pi (at^2 +bt +c)), or, in general, some kind of quadratically varying exponent, linear swept wave packet, or the like.
	www.wordiq.com /definition/Chirplet (1049 words)

	[No title]
		In particular, the many time-frequency (TF) methods, such as the Fourier transform, spectrogram, Wigner distribution, ambiguity function, wideband ambiguity function, and wavelet transform, may each be shown to be a special case of the chirplet transform.
		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).
	www.spie.org /web/journals/oe/oe_jun92.html (4608 words)

	Research of D.L. Jones' group
		These include adaptive window short-time Fourier transforms, adaptive wavelet transforms, adaptive optimal kernels, adaptive cone kernels, and fast algorithms for their computation.
		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.
		Performed the first accurate analysis of the computational complexity of the Hartley transform, showing conclusively that it is virtually equivalent to the real-valued FFT.
	www.ifp.uiuc.edu /~jones/research.html (1456 words)

	EyeTap Personal Imaging Lab (Site not responding. Last check: 2007-08-12)
		This paper is devoted to physical (intuitive) considerations of the chirplet transform.
		We then consider the use of multiple analyzing wavelets/windows, first to generalize Thomson's method of spectral estimation to the TF plane, and then to further generalize this result to the chirplet transform.
		The multiple analyzing wavelets/windows (which we call ``multiple mother chirplets'' when they are used in the latter context) collectively act to define a single ``tile'' in the TF plane, corresponding to each point in the chirplet transform parameter space.
	www.eyetap.org /research/wearables/wearcomp/chirplet/node4.html (214 words)

	A Successive Parameter Estimation Algorithm for Chirplet Signal Decomposition (Site not responding. Last check: 2007-08-12)
		The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate.
		Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB.
		To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed.
	www.ieee-uffc.org /archive/uffc/trans/Toc/abs/06/t06b2121.htm (267 words)

	Chirplet transform
		In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.
		(c) Thus the p-chirplet transform is often More appropriate than either the Fourier or wavelet transforms.
		Mihovilovic and R. Bracewell, "Adaptive chirplet representation of signals in the time-frequency plane," Electronics Letters 27 (13), 1159–1161 (20 June 1991).
	chirplet-transform.mindbit.com (1019 words)

	Technical Session 2
		Taxonomies of the various search and track modes are reported, and an example radar resource configuration is described in detail.
		One method to detect a moving target is to first reject the clutter and improve the SCR before the detection, such as the adaptive Fourier transform developed by Root when a target moves uniformly.
		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.
	www.ewh.ieee.org /r6/lac/radar02/papers/session2.html (366 words)

	The adaptive chirplet transform and visual evoked potentials.
		We propose a new approach based upon the adaptive chirplet transform (ACT) to characterize the time-dependent behavior of the visual evoked potential (VEP) from its initial transient portion (tVEP) to the steady-state portion (ssVEP).
		We also show that as few as three chirplets are required to represent a VEP response.
		Finally, we argue that the adaptive chirplet spectrogram gives a superior visualization of VEP signals' time-frequency structures when compared to the conventional spectrogram.
	www.galenicom.com /medline/article/16830941/mt:Motion%252520Perception (230 words)

	Quantitative Seismology: Advances in Studies of Fine-Scale Heterogeneities in a Deforming Earth VI Posters (Series 2) - ...
		The five-parameter chirplet atom is obtained from the unit Gaussian function by successive applications of scaling, fractional Fourier transform, time-shift and frequency-shift operators of various duration.
		In particular, the wide-range of TF methods such as the Fourier transform, spectrogram, Wigner distribution, and wavelet transform may each be shown to be a special case of the chirplet transform.
		Using the chirplet transform, each wave packet of the seismogram (mostly single component, sampling frequency = 150 Hz, duration = 15 s) is decomposed in terms of energy, arrival time, frequency, duration, shape (time-shear) and frequency modulation (frequency-shear).
	www.agu.org /meetings/fm04/fm04-sessions/fm04_S23B.html (10369 words)

	The Wavelet Digest :: View topic - Answer: Custom Designing Basis Functions
		Essentially finding the basis functions becomes searching based on MP in the dictionary formed by these chirplets It forms a redundant representation.
		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)

	The Chirplet Transform: Physical Considerations - Mann, Haykin (ResearchIndex)
		16 A generalised wavelet transform for Fourier analysis: the mu..
		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)

	IngentaConnect Characterization of seismic waveforms and classification of seism... (Site not responding. Last check: 2007-08-12)
		Characterization of seismic waveforms and classification of seismic events using chirplet atomic decomposition.
		In the present paper, we present a generalization of the wavelet transform, known as chirplet transform, specially designed to quantify the morphological attributes of individual seismic sections (packets) constituting the seismic waveforms.
		The proposed transform relies on an atomic decomposition of individual seismograms based on local multiscale chirps (swept frequency wave packets) of various shape and duration.
	www.ingentaconnect.com /content/bsc/gji/2006/00000166/00000002/art00016 (414 words)

	Chirp - Encyclopedia, History, Geography and Biography
		Chirplet transform — A signal representation based on a family of localized chirp functions, each member of which can usually be expressed as parameterized transformations of each other.
		This encyclopedia, history, geography and biography article about Chirp contains research on
		Chirp, Chirp modulation, Chirplet transform, See also and Signal processing.
	www.arikah.com /encyclopedia/Chirp (762 words)

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