Abstract:
The information about the Hilbert transform is often
scattered in books about signal processing. Their authors
frequently use mathematical formulas without explaining
them thoroughly to the reader.
The purpose of this research is to make a more stringent
presentation of the Hilbert transform but still with the
signal processing application in mind.
Everybody working in the field of singular integrals and
integral equations will know that during the last few
decades an entirely new mathematical field of Cauchy
principal value integrals and hypersingular integral has
developed.
Since this is a recent mathematical development, it is not
always easy for readers including academics, engineers
and researchers, to get a grap on.
Hilbert transforms deal with Calderon-Zygmund operators
and the theory of Calderon-Zygmund operators in such a
way that any body will be able to repeat the schedule use
of Hilbert transforms.
