Hilbert envelope bandwidth (Christof Faller )

Subject: Hilbert envelope bandwidth
From:    Christof Faller  <cfaller(at)AGERE.COM>
Date:    Mon, 27 Sep 2004 14:02:29 +0200

Dear list,

I am struggling with the following question:

Given a signal x(n) with
    X(f) = 0 for |f| < f1 or |f| > f2
    (bandpass filtered signal with bandwidth B = f2-f1)

e(n) is the Hilbert envelope of x(n) which can then be written as:
    x(n) = e(n)y(n),

where y(n) is the "temporally flattened" version of x(n).

The spectrum of e(n) satisfies:
   E(f) = 0 for |f| > f3

(Due to its DC offset, the evelope e(n) contains frequencies down to
zero).

==>
Can f3 be expressed as a function of B (the bandwidth of signal x)?

Any comments/suggestions are appreciated. Thanks,
   Christof Faller