Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Morlet_wavelet> ?p ?o. }
Showing items 1 to 25 of
25
with 100 items per page.
- Morlet_wavelet abstract "In mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision.In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as atoms, and which provide the best trade-off between spatial and frequency resolution. These are used in the Gabor transform, a type of short-time Fourier transform. In 1984, Jean Morlet introduced Gabor's work to the seismology community and, with Goupillaud and Grossmann, modified it to keep the same wavelet shape over equal octave intervals, resulting in the first formalization of the continuous wavelet transform. (See also Wavelet history)The wavelet is defined as a constant subtracted from a plane wave and then localised by a Gaussian window:where is defined bythe admissibility criterion and the normalisation constant is:The Fourier transform of the Morlet wavelet is:The "central frequency" is the position of the global maximum of which, in this case, is given by the solution of the equation:The parameter in the Morlet wavelet allows trade betweentime and frequency resolutions. Conventionally, the restriction is used to avoid problems with the Morlet wavelet at low (high temporal resolution).For signals containing only slowly varying frequency and amplitudemodulations (audio, for example) it is not necessary to use smallvalues of . In this case, becomes very small (e.g. ) and is, therefore, often neglected. Under the restriction , the frequency of the Morlet wavelet is conventionally taken to be .The wavelet exists as a complex version or a purely real-valued version. Some distinguish between the "real Morlet" vs the "complex Morlet". Others consider the complex version to be the "Gabor wavelet", while the real-valued version is the "Morlet wavelet".".
- Morlet_wavelet thumbnail MorletWaveletMathematica.svg?width=300.
- Morlet_wavelet wikiPageID "186963".
- Morlet_wavelet wikiPageRevisionID "580839130".
- Morlet_wavelet hasPhotoCollection Morlet_wavelet.
- Morlet_wavelet subject Category:Continuous_wavelets.
- Morlet_wavelet type Abstraction100002137.
- Morlet_wavelet type ContinuousWavelets.
- Morlet_wavelet type Event100029378.
- Morlet_wavelet type Happening107283608.
- Morlet_wavelet type Movement107309781.
- Morlet_wavelet type PsychologicalFeature100023100.
- Morlet_wavelet type Ripple107344663.
- Morlet_wavelet type Wave107352190.
- Morlet_wavelet type YagoPermanentlyLocatedEntity.
- Morlet_wavelet comment "In mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision.In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as atoms, and which provide the best trade-off between spatial and frequency resolution.".
- Morlet_wavelet label "Morlet wavelet".
- Morlet_wavelet sameAs Morletova_vlnka.
- Morlet_wavelet sameAs m.019ks0.
- Morlet_wavelet sameAs Q3505077.
- Morlet_wavelet sameAs Q3505077.
- Morlet_wavelet sameAs Morlet_wavelet.
- Morlet_wavelet wasDerivedFrom Morlet_wavelet?oldid=580839130.
- Morlet_wavelet depiction MorletWaveletMathematica.svg.
- Morlet_wavelet isPrimaryTopicOf Morlet_wavelet.
