You can think of the transform as a function that produces a 90 degree phase shift with a constant gain. For negative frequencies, the rotation is 90 degrees and for positive frequencies, the ...

You can think of the transform as a function that produces a 90 degree phase shift with a constant gain. For negative frequencies, the rotation is 90 degrees and for positive frequencies, the ...

For the shift operator corresponding to the Hilbert transform we use Bellman function methods; however, there is now a general theorem for a class of Haar shift operators that can be used instead to ...

Jonathan M. Bennett, Hilbert Transforms and Maximal Functions along Variable Flat Curves, Transactions of the American Mathematical Society, Vol. 354, No. 12 (Dec., 2002), pp. 4871-4892 Free online ...