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Chirplet
In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.S. Mann and S. Haykin,The Chirplet transform: A generalization of Gabor's logon transform, ''Proc. Vision Interface 1991'', 205–212 (3–7 June 1991).D. Mihovilovic and R. N. Bracewell, "Adaptive chirplet representation of signals in the time–frequency plane," ''Electronics Letters'' 27 (13), 1159–1161 (20 June 1991). 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 Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirp
A chirp is a signal in which the frequency increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser systems, and to other applications, such as in spread-spectrum communications (see chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components). It is usually compensated for by using a matched filter, which can be part of the propagation channel. Depending on the specific performance measure, however, there are better techniques both for radar and communication. Since it was used in radar and space, it has been adopted also for communication standards. For automotive radar applications, it is usually called linear frequency modulated waveform (LFMW). In spread-spectrum usage, surface acoustic wave (SA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mother Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the Middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including but not limited to aud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractional Fourier Transform
In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. 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 any ''intermediate'' domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition. The FRFT can be used to define fractional convolution, correlation, and other operations, and can also be further generalized into the linear canonical transformation (LCT). An early definition of the FRFT was introduced by Condon, by solving for the Green's function for phase-space rotations, and also by Namias, generalizing work of Wiener on Hermite polynomials. However, it was not widely recognized in signal processing until it was independently reintroduced around 1993 by several groups. Since th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the Middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including but not limited to au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steve Mann (inventor)
William Stephen George Mann (born 8 June 1962) is a Canadian engineer, professor, and inventor who works in augmented reality, computational photography, particularly wearable computing, and high-dynamic-range imaging. Mann is sometimes labeled the "Father of Wearable Computing" for early inventions and continuing contributions to the field.Tech Giant "Father of Wearable Tech" Steve Mann "Goes for The Ride" to YYD ROBO!, YYD Corporate News, 2017-07-31"Father of Wearable Computing, Steve Mann, to Keynote FITC Wearables", by Nikolas Badminton, 2014-11-11, Toronto, Medium He cofounded InteraXon, makers of the Muse brain-sensing headband, and is also a founding member of the IEEE Council on Extended Intelligence (CXI). Mann is currently CTO and cofounder at Blueberry X Technologies and Chairman of MannLab. Mann was born in Canada, and currently lives in Toronto, Canada, with his wife and two children. Early life and education Mann holds a PhD in Media Arts and Sciences (1997) from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radar
Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the objects. Radio waves (pulsed or continuous) from the transmitter reflect off the objects and return to the receiver, giving information about the objects' locations and speeds. Radar was developed secretly for military use by several countries in the period before and during World War II. A key development was the cavity magnetron in the United Kingdom, which allowed the creation of relatively small systems with sub-meter resolution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time–frequency Representation
A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or "energy density" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase. Background and motivation A signal, as a function of time, may be considered as a representation with perfect ''time resolution''. In contrast, the magnitude of the Fourier transform (FT) of the signal may be considered as a representation with perfect ''spectral resolution'' but with no time information because the magnitude of the FT conveys frequency content but it fails to convey when, in ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time–frequency Analysis
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains ''simultaneously,'' using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform. The mathematical motivation for this study is that functions and their transform representation are tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform – and the fact that two-fold Fourier transform reverses direction – can be in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transforms
Transform may refer to: Arts and entertainment * Transform (scratch), a type of scratch used by turntablists * ''Transform'' (Alva Noto album), 2001 * ''Transform'' (Howard Jones album) or the title song, 2019 * ''Transform'' (Powerman 5000 album) or the title song, 2003 * ''Transform'' (Rebecca St. James album), 2000 * ''Transform'' (single album), by Teen Top, or the title song, 2011 *"Transform", a song by Daniel Caesar from ''Freudian'', 2017 *"Transform", a song by Your Memorial from ''Redirect'', 2012 Mathematics, science, and technology Mathematics * Tensor transformation law, a defining property of tensors *Tensor product model transformation, numerical method applied to control theory *Transformation (function), concerning functions from sets to themselves * Transform theory, theory of integral transforms ** List of transforms, a list of mathematical transforms **Integral transform, a type of mathematical transform Computer graphics *Transform coding, a type of data comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet Transform
In mathematics, a wavelet series is a representation of a square-integrable ( real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. Definition A function \psi \,\in\, L^2(\mathbb) is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space L^2\left(\mathbb\right) of square integrable functions. The Hilbert basis is constructed as the family of functions \ by means of dyadic translations and dilations of \psi\,, :\psi_(x) = 2^\frac \psi\left(2^jx - k\right)\, for integers j,\, k \,\in\, \mathbb. If under the standard inner product on L^2\left(\mathbb\right), :\langle f, g\rangle = \int_^\infty f(x)\overlinedx this family is orthonormal, it is an orthonormal system: :\begin \langle\psi_,\psi_\rangle &= \int_^\infty \psi_(x)\overl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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