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Analysis Mathematica, 1987
Для любой функцииf∈L p (|x|αdx, гд е p >1, аа — любое действительное числ о, найдены необходимые и достаточные услови я для того, чтобы ее преобразова ние ГильбертаHf $$Hf(x) = \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty (x - t)^{ - 1} f(t)dt, x \in ( - \infty ,\infty )$$ , также принадлежалоL p (|x|)αdx.L p (|x|)αdx — класс ...
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Для любой функцииf∈L p (|x|αdx, гд е p >1, аа — любое действительное числ о, найдены необходимые и достаточные услови я для того, чтобы ее преобразова ние ГильбертаHf $$Hf(x) = \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty (x - t)^{ - 1} f(t)dt, x \in ( - \infty ,\infty )$$ , также принадлежалоL p (|x|)αdx.L p (|x|)αdx — класс ...
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2009
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader.
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The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader.
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Boehmians and Their Hilbert Transforms
Integral Transforms and Special Functions, 2002Let {\cal D} denote the space of test functions on R and {\cal D}^\prime the space of Schwartz distributions. Let H({\cal D}) and H({\cal D}^\prime) denote the images of {\cal D} and {\cal D}^\prime under the usual Hilbert transform. A suitable topology can be introduced in H({\cal D}) so that continuous linear functionals on this space denoted by H ...
V. Karunakaran, R. Roopkumar
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Hilbert-Transformation (HT) [PDF]
, 1985 In Aufgabe A7.1 wird die HT im Zeitbereich angewendet, auserdem wird der „Hilbert-Transformator“ eingefuhrt, dessen Impuls- und Sprungantwort in weiteren Aufgaben dieses Kapitels Anwendung findet. Die HT im Frequenzbereich verbindet Real- und Imaginarteil der Ubertragungsfunktion eines realisierbaren Systems. Dies wird in 7.2 naher untersucht.
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2010
Publisher Summary This chapter focuses on a generalized way of treating narrow-banded processes from mathematical and physical points of view using the Hilbert transform. The methods described are not limited to narrow-banded processes but work perfectly well for broad-banded spectra as well. When working with theoretical or experimental wave trains,
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Publisher Summary This chapter focuses on a generalized way of treating narrow-banded processes from mathematical and physical points of view using the Hilbert transform. The methods described are not limited to narrow-banded processes but work perfectly well for broad-banded spectra as well. When working with theoretical or experimental wave trains,
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Frontiers of Mathematics in China, 2013
We introduce a space Open image in new window , where Open image in new window is the testing function space whose functions are infinitely differentiable and have bounded support, and Open image in new window is the space the double Hilbert transform acting on the testing function space.
Xiaona Cui, Rui Wang, Dunyan Yan
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We introduce a space Open image in new window , where Open image in new window is the testing function space whose functions are infinitely differentiable and have bounded support, and Open image in new window is the space the double Hilbert transform acting on the testing function space.
Xiaona Cui, Rui Wang, Dunyan Yan
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Summability to the Hilbert Transform
2021New sufficient conditions for the almost everywhere convergence (at the Lebesgue points) of general summability means of the conjugate integral to the Hilbert transform are obtained in the paper. Consequences and applications are also discussed.
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1999
In diesem Kapitel wollen wir uns mit einer Transformation befassen, die in der Modulationstheorie eine grose Rolle spielt: durch geeignete Erganzung des ursprunglichen Signals x(t) zu einem sogenannten analytischen Signal z(t) = x(t) – jy(t) erhalt man eine komplexe Zeitfunktion mit einseitigem Spektrum. Dies geschieht dadurch, das man y(t) als Hilbert-
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In diesem Kapitel wollen wir uns mit einer Transformation befassen, die in der Modulationstheorie eine grose Rolle spielt: durch geeignete Erganzung des ursprunglichen Signals x(t) zu einem sogenannten analytischen Signal z(t) = x(t) – jy(t) erhalt man eine komplexe Zeitfunktion mit einseitigem Spektrum. Dies geschieht dadurch, das man y(t) als Hilbert-
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The discrete Hilbert transform
Proceedings of the IEEE, 1970A Hilbert transformation procedure for discrete data has been developed. This transform could be useful in a variety of applications such as the analysis of sampled data systems and the simulation of filters.
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