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Inverse of Hilbert transform

Started by carlierm January 5, 2010
Hi,

I need to extract the envelope of an audio signal and do some changes in
its spectum of magnitude, and then I need to reconstruct the signal and
take it to the time domain.  I thing thatt I can do that taking the hilbert
transform of the original signal,  find the magnitu and perform the
changes; but what i do not know is how to go back to the time domain.  How
to take the inverse of the hilbert transform? Any sugestions? 

I will appreciate very much any help.

Monica

On Tue, 05 Jan 2010 16:26:06 -0600, carlierm wrote:

> Hi, > > I need to extract the envelope of an audio signal and do some changes in > its spectum of magnitude, and then I need to reconstruct the signal and > take it to the time domain. I thing thatt I can do that taking the > hilbert transform of the original signal, find the magnitu and perform > the changes; but what i do not know is how to go back to the time > domain. How to take the inverse of the hilbert transform? Any > sugestions? > > I will appreciate very much any help. > > Monica
(A) Unless I'm quite mistaken, the Hilbert transform is it's own inverse, give or take a sign change -- since it is defined as that which shifts the phase of all components with positive frequencies by +90 degrees, and the phase of all components with negative frequencies by -90 degrees, doing it again will get you the negative of what you started out with. (B) A Hilbert-transformed signal already is in the time domain. (C) What is your end goal? You obviously are confused about the bark on the tree you're inspecting -- do you know the shape of your forest? -- www.wescottdesign.com
carlierm wrote:
> Hi, > > I need to extract the envelope of an audio signal and do some changes in > its spectum of magnitude, and then I need to reconstruct the signal and > take it to the time domain. I thing thatt I can do that taking the hilbert > transform of the original signal, find the magnitu and perform the > changes; but what i do not know is how to go back to the time domain. How > to take the inverse of the hilbert transform? Any sugestions? > > I will appreciate very much any help.
The "envelope" of an audio signal is not (as far as I know) a well defined term. If you could explain what you mean by it, I'll try to answer you. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
>On Tue, 05 Jan 2010 16:26:06 -0600, carlierm wrote: > >> Hi, >> >> I need to extract the envelope of an audio signal and do some changes
in
>> its spectum of magnitude, and then I need to reconstruct the signal
and
>> take it to the time domain. I thing thatt I can do that taking the >> hilbert transform of the original signal, find the magnitu and
perform
>> the changes; but what i do not know is how to go back to the time >> domain. How to take the inverse of the hilbert transform? Any >> sugestions? >> >> I will appreciate very much any help. >> >> Monica > >(A) Unless I'm quite mistaken, the Hilbert transform is it's own >inverse, give or take a sign change -- since it is defined as that which
>shifts the phase of all components with positive frequencies by +90 >degrees, and the phase of all components with negative frequencies by -90
>degrees, doing it again will get you the negative of what you started out
>with. > >(B) A Hilbert-transformed signal already is in the time domain. > >(C) What is your end goal? You obviously are confused about the bark on
>the tree you're inspecting -- do you know the shape of your forest? > >-- >www.wescottdesign.com
I've used a check that 4 Hilberts in a row gets you roughly where you started as a sanity test for a Hilbert implementation. Steve
On Jan 5, 5:26=A0pm, "carlierm" <carliermon...@gmail.com> wrote:
> Hi, > > I need to extract the envelope of an audio signal and do some changes in > its spectum of magnitude, and then I need to reconstruct the signal and > take it to the time domain. =A0I thing thatt I can do that taking the hil=
bert
> transform of the original signal, =A0find the magnitu and perform the > changes; but what i do not know is how to go back to the time domain. =A0=
How
> to take the inverse of the hilbert transform? Any sugestions? > > I will appreciate very much any help. > > Monica
H^-1(f(t)) =3D -H(f(t))
On Tue, 05 Jan 2010 18:58:56 -0600, "steveu" <steveu@coppice.org>
wrote:

  [Snipped by Lyons]
> >I've used a check that 4 Hilberts in a row gets you roughly where you >started as a sanity test for a Hilbert implementation. > >Steve
Hi, right you are! And three Hilbert transforms in a row yields the inverse Hilbert transform. [-Rick-]
Clay wrote:
> On Jan 5, 5:26 pm, "carlierm" <carliermon...@gmail.com> wrote: >> Hi, >> >> I need to extract the envelope of an audio signal and do some changes in >> its spectum of magnitude, and then I need to reconstruct the signal and >> take it to the time domain. I thing thatt I can do that taking the hilbert >> transform of the original signal, find the magnitu and perform the >> changes; but what i do not know is how to go back to the time domain. How >> to take the inverse of the hilbert transform? Any sugestions? >> >> I will appreciate very much any help. >> >> Monica > > H^-1(f(t)) = -H(f(t))
Clay, maybe you can tell me what the envelope of an audio signal -- say, the output of a microphone -- is. I imagine it as the output as a VU meter, but that doesn't fit the question. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Jan 6, 2:54=A0pm, Jerry Avins <j...@ieee.org> wrote:
> Clay wrote: > > On Jan 5, 5:26 pm, "carlierm" <carliermon...@gmail.com> wrote: > >> Hi, > > >> I need to extract the envelope of an audio signal and do some changes =
in
> >> its spectum of magnitude, and then I need to reconstruct the signal an=
d
> >> take it to the time domain. =A0I thing thatt I can do that taking the =
hilbert
> >> transform of the original signal, =A0find the magnitu and perform the > >> changes; but what i do not know is how to go back to the time domain. =
=A0How
> >> to take the inverse of the hilbert transform? Any sugestions? > > >> I will appreciate very much any help. > > >> Monica > > > H^-1(f(t)) =3D -H(f(t)) > > Clay, maybe you can tell me what the envelope of an audio signal -- say, > the output of a microphone -- is. I imagine it as the output as a VU > meter, but that doesn't fit the question. > > Jerry > -- > Engineering is the art of making what you want from things you can get.- =
Hide quoted text -
> > - Show quoted text -
Yes it is like a VU meter. Of course for standard AM, the envelope minus the DC offset is the data of interest. I don't know all of what the OP desires, so we'll have to wait on more clarification. With Hilbert transforms being mentioned, one assumes analytic signals are involved and then the magnitude of the analytic signal is the instantaneous amplitude. The OP mentions some intermediate operations before the inverse Hilbert is applied, so who knows? Clay