[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: Hilbert envelope bandwidth

You may have a look at pp 796-798 of the book A.V. Oppenheim, and R. W.
Schafer, "Discrete-time Signal Processig", Second Edition, which deals with
the representation of bandpass signals in the Hilbert domain. The picture
depicted there explains everything.
Hope this can help !

-----Message d'origine-----
De : AUDITORY Research in Auditory Perception
[mailto:AUDITORY@LISTS.MCGILL.CA]De la part de Christof Faller
Envoye : 27 septembre 2004 08:02
Objet : 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