The functions described in this section compute a discrete-time
analytic signal from a real data sequence using the Hilbert transform. The analytic
signal is a complex signal whose real part is a replica of the original data, and
imaginary part contains the Hilbert transform. That is, the imaginary part is a version
of the original real data with a 90 degrees phase shift. The Hilbert transformed data
have the same amplitude and frequency content as the original real data, plus the
additional phase information.