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Re: Hilbert envelope bandwidth

If bandwidth of bandpass filtered signal  is B


The envelope (as defiend by Hilbert transform), log-envelope,
instantaneous frequency (time derivative of phasee) are not

But it can be shown that: envelope squre and intensity weighted
instantaneous frequency (IWIF) are bandlimited with bandwidth = B.



Yadong Wang,  Postdoctoral Fellow
Cognitive Neuroscience of Language Lab
Dept. of Linguistics
1401 Marie Mount Hall
University of Maryland
College Park MD 20742

(o) (301) 405-2587

-----Original Message-----
From: AUDITORY Research in Auditory Perception
[mailto:AUDITORY@LISTS.MCGILL.CA] On Behalf Of Christof Faller
Sent: Monday, September 27, 2004 7:02 AM
Subject: Hilbert envelope bandwidth

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

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

Any comments/suggestions are appreciated. Thanks,
   Christof Faller