A distribution space for Hilbert transform and its applications |
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Authors: | LiHua Yang |
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Institution: | (1) School of Mathematics and Computing Science, Sun Yat-Sen University, Guangzhou, 510275, China |
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Abstract: | In this paper, a new distribution space
is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that
is the biggest subspace of
on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L
p
functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations
of the space
are given and a class of useful nonlinear phase signals is shown to be in
. Finally, the applications of the extended Hilbert transform are discussed.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 60475042, 10631080) |
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Keywords: | Hilbert transform distribution time-frequency analysis |
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