DISCERETE-TIME ANALYTIC SIGNALS WITH IMPROVED SHIFTABILITY
M.Sc Thesis
Mohamed Elfataoui
February 2004
Thesis (ps) / Thesis(pdf)
In this thesis, we propose two methods for generating a discrete-time
analytic (DTA) signal. This first is in the frequency domain and the
second in the time domain.
We consider a common procedure in MATLAB for generating DTA signals
and show how it fails for specific discrete-time signals. A new
frequency domain technique is formulated that resovles this defect.
Both methods have the same redundancy. The new analytic signal
preserves the original signal (real part) as also the zeros of
its discrete spectrum in the negative frequencies. The superiority of the
new method is in the introduction of one additional zero of
the continuous spectrum of the original signal at a negative
frequency. There is a corresponding improvement in shiftability
but at a loss of orthogonality.
We also formulate a new time-domain method for DTA signal
generation. The advantage of this technique is that it provides
linear phase, orthogonality, invertibility and real-time implementation.
Furthermore, we can also obtain improved shiftability. To our
knowledge, no other technique for DTA signal generation provides
all these properties.