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Hilbert transform

   Also found in: Wikipedia 0.02 sec.
Hilbert transform [′hil·bərt ¦tranz‚fȯrm]
(mathematics)
The transformF(y) of a function ƒ(x) realized by taking the Cauchy principal value of the integral over the real numbers of (1/π)f(ƒ)[1/(x-y


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C] denotes respectively, the maximal function, the Hilbert integral, the maximal Hilbert transform and the Carleson operator.
To distinguish between these different types of modulations, the Hilbert transform is used to compute the amplitude envelopes of the signals, which are then filtered between 0.
The mathematicians investigate the pointwise convergence of weighted averages linked to averages along cubes, divergent ergodic averages along the squares, the one-sided ergodic Hilbert transform, deterministic walks in Markov environments with constant rigidity, limit theorems for sequential expanding dynamical systems, and random Fourier-Stieltjes transforms.
 
 
 
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