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In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t). The Hilbert transform is given by the Cauchy principal value of the convolution with the function 1 / ( π t ) {\displaystyle 1/(\pi t)} (see § Definition). The…
History, Properties & Hilbert transform in signal processing
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Hilbert transform | is a | specific singular integral that takes a function | 0.90 | text |
| Hilbert transform | is a | bounded operator on L p | 0.90 | text |
| Hilbert transform | is a | multiplier operator | 0.90 | text |
| Hilbert transform | is a | bounded operator from L1 to L1 | 0.90 | text |
| Hilbert transform | is a | anti-self adjoint operator relative to the duality pairing between L p | 0.90 | text |
| Hilbert transform | is a | anti-involution | 0.90 | text |
| Hilbert transform | is a | Hilbert transform of the derivative | 0.90 | text |
| Hilbert transform | is a | only bounded operator on L2 with these properties.In fact there is a wider set of operators that commute with the Hilbert transform | 0.90 | text |
| Hilbert transform | is a | extension of the discrete Hilbert transform to integers modulo an appropriate prime number | 0.90 | text |
| Hilbert transform | related to Anti-self adjointness | The Hilbert | 0.60 | section |
| Hilbert transform | related to Anti-self adjointness | Hölder | 0.60 | section |
| Hilbert transform | related to Anti-self adjointness | Symbolically | 0.60 | section |
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