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hilbert_transform [2014/02/21 18:36] nikolaj |
hilbert_transform [2014/03/21 11:11] (current) |
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===== Hilbert transform ===== | ===== Hilbert transform ===== | ||
==== Partial Function ==== | ==== Partial Function ==== | ||
- | | @#FFBB00: $H: (\mathbb C\to\mathbb C)\to(\mathbb C\to\mathbb C)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $H: (\mathbb C\to\mathbb C)\to(\mathbb C\to\mathbb C)$ | |
- | | @#FFBB00: $H(f):=y\mapsto \frac{1}{\pi}\cdot\mathcal P\int_{-\infty}^\infty\frac{f(x)}{y-x}\,\mathrm dx$ | | + | | @#FFBB00: definiendum | @#FFBB00: $H(f):=y\mapsto \frac{1}{\pi}\cdot\mathcal P\int_{-\infty}^\infty\frac{f(x)}{y-x}\,\mathrm dx$ | |
==== Discussion ==== | ==== Discussion ==== |