Top 10 similar words or synonyms for hilbert_transform

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Top 30 analogous words or synonyms for hilbert_transform

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Hilbert transform For example, the Hilbert transform leads to the harmonic conjugate of a given function in Fourier analysis, aka harmonic analysis. Equivalently, it is an example of a singular integral operator and of a Fourier multiplier.
Hilbert transform When the Hilbert transform is applied twice in succession to a function "u", the result is negative "u":
Hilbert transform provided the integrals defining both iterations converge in a suitable sense. In particular, the inverse transform is −"H". This fact can most easily be seen by considering the effect of the Hilbert transform on the Fourier transform of "u"("t") (see Relationship with the Fourier transform, below).
Hilbert transform An extensive table of Hilbert transforms is available ().
Hilbert transform Note that the Hilbert transform of a constant is zero.
Hilbert transform exists for almost every "t". The limit function is also in "L"(R) and is in fact the limit in the mean of the improper integral as well. That is,
Hilbert transform The Hilbert transform has the following invariance properties on "L"(R).
Hilbert transform Interpreted naïvely, the Hilbert transform of a bounded function is clearly ill-defined. For instance, with "u" = sgn("x"), the integral defining "H"("u") diverges almost everywhere to ±∞. To alleviate such difficulties, the Hilbert transform of an "L"-function is therefore defined by the following regularized form of the integral
Hilbert transform Furthermore, there is a unique harmonic function "v" defined in the upper half-plane such that "F"("z") = "u"("z") + i"v"("z") is holomorphic and
Hilbert transform This harmonic function is obtained from "f" by taking a convolution with the conjugate Poisson kernel