A Frequency Domain Method for Generation of Discrete Time Analytic Signals
M. Elfataoui and Gagan Mirchandani
(Paper (pdf)
We consider a common frequency domain procedure {\em hilbert} for
generating discrete-time analytic signals and show how it fails for a
specific class of signals. A new frequency domain technique {\em
ehilbert} is formulated that solves the defect. Moreover, the new
technique is applicable to all discrete-time real signals of even
length. It is implemented by the introduction of one additional zero
of the continuous spectrum of the analytic signal {\em hilbert} at a
negative frequency. Both frequency-domain methods have the same
redundancy. The new analytic signal preserves the original signal
(real part) and also the zeros of the discrete spectrum {\em hilbert}
in the negative frequencies. The greater attenuation at the negative
frequencies affects the degree of aliasing of the analytic signal. It
is measured by applying the analytic signal to an orthogonal wavelet
transform and determining the improved transform shiftability.