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In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Image File history File links wave, wavelet, chirp, chirplet I took this picture off the computer screen of a realtime 3d data visualizer that I did with Shawn Becker on special purpose 3d rendering hardware, to visualize my idea of using chirps as analysis primitives (i. ...
Image File history File links wave, wavelet, chirp, chirplet I took this picture off the computer screen of a realtime 3d data visualizer that I did with Shawn Becker on special purpose 3d rendering hardware, to visualize my idea of using chirps as analysis primitives (i. ...
The concept wave is related to a disturbance that propagates through space, often transferring energy. ...
In mathematics, 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). ...
A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. ...
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. ...
Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ...
// Definition Inner Product of two vectors Given twoN-by-1 column vectors v and u, the inner product is defined as the scalar quantity α resulting from where or equivalently indicates the conjugate transpose operator applied to vector v. ...
Similarity to other transforms Much as in the wavelet transform, the 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). The wavelet transform is a transformation to basis functions that are localized in scale and in time as well (where the Fourier transform is only localized in frequency, never giving any information about where in space or time the frequency happens). ...
What is a chirplet? The term "chirplet" was reportedly coined by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell in the 1980s to describe a windowed portion of a chirp function. In his words, 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 transforms) or wavelets. Steve Mann (born 1962) is a professor in the Department of Electrical and Computer Engineering at the University of Toronto. ...
A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. ...
The short-time Fourier transform (STFT), or short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of a signal as it changes over time. ...
In mathematics, 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). ...
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" as such was in Mann and Haykin (1991), describing the Gaussian chirplet transform together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term "chirplet" (but not "chirplet transform") was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year. M*A*S*H , see Corporal Walter (Radar) OReilly. ...
Generally, the word gaussian pertains to Carl Friedrich Gauss and his ideas. ...
Ronald Newbold Bracewell (1921 – ) is the Lewis M. Terman Professor of Electrical Engineering, Emeritus of the Space, Telecommunications and Radioscience Laboratory at Stanford University. ...
Applications
 (a) In image processing, periodicity is often subject to a linear scaling. (b) In this image, repeating structures like the alternating dark space inside the windows, and light space of the white cement, "chirp" (increase in frequency) towards the right. (c) The chirplet transform is more useful than either the unadjusted Fourier or wavelet transforms. The chirplet transform is a useful signal analysis and representation framework that is widely used in Image File history File links p-type chirplets are useful for image processing I took this picture of the red building and drew a graph through it, to show the chirplet transform, how projective (p-type) chirps operate. ...
Image File history File links p-type chirplets are useful for image processing I took this picture of the red building and drew a graph through it, to show the chirplet transform, how projective (p-type) chirps operate. ...
SETI@home uses chirp functions to compensate for Doppler drift. M*A*S*H , see Corporal Walter (Radar) OReilly. ...
Health science is the discipline of applied science which deals with human and animal health. ...
Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
SETI@home logo SETI@home (SETI at home) is a grid computing (distributed computing in the projects own terminology) project using Internet-connected computers, hosted by the Space Sciences Laboratory, at the University of California, Berkeley, in the United States. ...
Taxonomy of chirplet transforms There are two broad categories of chirplet transform: These categories may be further subdivided by: - choice of chirp
- choice of window
In either the fixed or adaptive case, the chirplets may be: - q-chirplets (quadratic chirplets) of the form exp(i 2π (a t2 + b t + c)) or, in general, some kind of quadratically varying exponent, linear swept wave packet, or the like. These are sometimes called linear FM chirplets (linear frequency-modulated chirplets, since quadratic phase is linear frequency). Commonly used families of q-chirplets are metaplectomorphisms of one another (i.e. the energy distribution of any member of the family of q-chirplets can be generated from any other member by shear-in-time, shear-in-frequency, dilation, translation-in-time, and translation-in-frequency).
- w-chirplets, also known as warblets. A family of warblets are like the sound made by birds called warblers. Unwindowed warblets have a sinusoidally varying time-frequency distribution, or similar cyclostationary or periodically varying time-frequency plot. The sound of a police siren is an example, in which the pitch goes up and down periodically. Of course the warblet is a "piece of" a warble (i.e. a windowed section of something that has a time-frequency periodicity).
- d-chirplets, also known as Doppler chirplets. These are analysis functions that mimic the Doppler shift of a passing tone, e.g. the sound you hear from a train whistle as it moves past.
- p-chirplets, in which the scale varies projectively. 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).
The choice of window is also another matter of decision. A Gaussian window is one possible choice, leading to a four parameter chirplet transform (for which time-shear and frequency-shear only give one degree of freedom that may thus be encapsulated as rotation angle --- Radon transform of the Wigner distribution may, for example, be used, as may the fractional Fourier transform). In mathematics and signal processing, a metaplectomorphism is a transformation by way of an operator from a metaplectic group of operators. ...
There are three groups of passerine birds, order Passeriformes, which are called warblers. ...
The Doppler effect is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves. ...
In signal processing, a window function (or apodization function) is a function that is zero-valued outside of some chosen interval. ...
In mathematics, the Radon transform in two dimensions is the integral transform The Radon transform integrates a function over lines in the plane, mapping a function of position to a function of the slope and the y-intercept. ...
Wigner distribution can refer to two things: Wigner semicircle distribution - A probability function (Eugene Wigner) Wigner-Ville distribution - A time-frequency representation (Hermann Wigner) ...
Another possible choice is the rectangular window, and of course, discrete prolate spheroidal sequences may be used, by way of the "method of multiple mother chirplets". This method gives a total chirplet transform as the sum of energies in various contributant chirplet transforms made from multiple windows, akin to the way in which DPSSs are used to get a perfect rectangular tiling of the time-frequency plane. Thus it is now possible to get perfect parallelogram tiling of the time-frequency plane, using the method of multiple mother chirplets.
Related work The chirplet transform is a generalized representation that includes as special cases: Josef Segman proposed the idea of incorporating scale into the Heisenberg group (position, momentum, phase, or equivalently any canonical conjugate variables taken together with phase, such as, for example, time, frequency, and phase). This gave rise to a four parameter space of time, frequency, phase, and scale. Segman introduced this idea of "phase scale". (Personal communication with Mann, from Josef Segman, at Harvard University and at Massachusetts Institute of Technology). Further personal communication between Irving Segal (the principal behind the Segal, Shale Weil representation, known also as the metaplectic representation --- a double covering of the symplectic group) and Mann led to additional insight into the chirplet transform, in particular, to the variation of the chirplet transform that is based on q-chirplets. The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i. ...
The short-time Fourier transform (STFT), or short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of a signal as it changes over time. ...
The Wigner quasi-probability distribution was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics. ...
The wavelet transform is a transformation to basis functions that are localized in scale and in time as well (where the Fourier transform is only localized in frequency, never giving any information about where in space or time the frequency happens). ...
Canonical conjugate variables in physics are pairs of variables that share an uncertainty relation. ...
The Segal-Shale-Weil distribution is a distribution based on metaplectomorphisms of a plane of two canonical conjugate variables; such as time and frequency. ...
Harvard University is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ...
The Massachusetts Institute of Technology, or MIT, is a university located in the city of Cambridge, Massachusetts, USA. MIT is one of the worlds leading research institutions in science and technology, as well as in numerous other fields, including management, economics, linguistics, political science, and philosophy. ...
Irving Ezra Segal (1918-1998) was a mathematician known for work on theoretical quantum mechanics. ...
In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. ...
In mathematics, the name symplectic group can refer to two different, but closely related, types of mathematical groups. ...
Further ongoing work Work on the chirplet transform is ongoing. One of the most exciting developments is that of Richard Cui, who has developed a chirplet-based Brain Computer Interaction system that allows a person wearing eyetap eyeglasses to interact with a computer by way of Visual Evoked Potentials. Chirplet-based VEP is the subject of Richard Cui's PhD thesis. The EyeTap is a device which allows the eye itself to function as both a display and a camera. Eyetap devices measure the quantity of light in each of a large number of rays of light that converge into at least one eye of the wearer, and then resynthesize these...
Various companies, such as Andromed, National Instruments, etc., use and support the chirplet transform in a wide range of product offerings.
See also Other time-frequency transforms: The short-time Fourier transform (STFT), or short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of a signal as it changes over time. ...
The wavelet transform is a transformation to basis functions that are localized in scale and in time as well (where the Fourier transform is only localized in frequency, never giving any information about where in space or time the frequency happens). ...
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. ...
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