# Re: Hilbert envelope bandwidth

```I would think that it would simply be (f2-f1)/2. It should atleast
be true if the spectrum is symmetrical around (f2+f1)/2. I am not sure
what would happen if the spectrum is not symmetrical around (f2+f1)/2.
Please correct me if I am wrong.

Tarun

On Mon, 27 Sep 2004, Christof Faller wrote:

> 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
>

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Tarun Pruthi