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 ...

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 ...

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 ...