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- Modulation_space abstract "Modulation spaces are a family of Banach spaces defined by the behavior of the short-time Fourier transform withrespect to a test function from the Schwartz space. They were originally proposed by Hans Georg Feichtinger and are recognized to be the right kind of function spaces for time-frequency analysis. Feichtinger's algebra, while originally introduced as a new Segal algebra, is identical to a certain modulation space and has become a widely used space of test functions for time-frequency analysis.Modulation spaces are defined as follows. For , a non-negative function on and a test function , the modulation space is defined byIn the above equation, denotes the short-time Fourier transform of with respect to evaluated at . In other words, is equivalent to . The space is the same, independent of the test function chosen. The canonical choice is a Gaussian.".
- Modulation_space wikiPageID "31978882".
- Modulation_space wikiPageRevisionID "585990395".
- Modulation_space hasPhotoCollection Modulation_space.
- Modulation_space subject Category:Banach_spaces.
- Modulation_space type Abstraction100002137.
- Modulation_space type Attribute100024264.
- Modulation_space type BanachSpaces.
- Modulation_space type Space100028651.
- Modulation_space comment "Modulation spaces are a family of Banach spaces defined by the behavior of the short-time Fourier transform withrespect to a test function from the Schwartz space. They were originally proposed by Hans Georg Feichtinger and are recognized to be the right kind of function spaces for time-frequency analysis.".
- Modulation_space label "Modulation space".
- Modulation_space sameAs Modulationsräume.
- Modulation_space sameAs m.0gvry0p.
- Modulation_space sameAs Q6889770.
- Modulation_space sameAs Q6889770.
- Modulation_space sameAs Modulation_space.
- Modulation_space wasDerivedFrom Modulation_space?oldid=585990395.
- Modulation_space isPrimaryTopicOf Modulation_space.