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hilbert_transform [2014/02/21 18:22] nikolaj |
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| - | ===== Hilbert transform ===== | ||
| - | ==== Partial Function ==== | ||
| - | | @#FFBB00: $H: (\mathbb C\to\mathbb C)\to(\mathbb C\to\mathbb C)$ | | ||
| - | | @#FFBB00: $H(f):=t\mapsto \frac{1}{\pi}\cdot\mathcal P\int_{-\infty}^\infty\frac{f(\tau)}{t-\tau}\,\mathrm dx$ | | ||
| - | ==== Discussion ==== | ||
| - | $H(H(f))=-f$ | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Hilbert_transform|Hilbert transform]] | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Cauchy principal value]] | ||
