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Discrete-time analytic signal computation of a real signal using Hilbert transform
real vector : the real signal samples
Complex vector: the discrete-time analytic signal.
Returns theanalytic signal, from a real data sequence.
The analytic signal
x= xr + i*xi has a real part,
is the original data, and an imaginary part,
xi, which contains
the Hilbert transform. The imaginary part is a version of the
original real sequence with a 90° phase shift.
Marple, S.L., "Computing the discrete-time analytic signal via FFT," IEEE Transactions on Signal Processing, Vol. 47, No.9 (September 1999), pp.2600-2603