how to handle negative inst. frequencies from hilbert transform?

Just wondering how one practically handles negative frequencies
obtained from estimating the instantaneous frequency using the Hilbert
Transform.

Here is what I am doing:

(1) take a time series (e.g., speech phoneme or two), x
(2) compute analytic signal, X = hilbert(x);
(3) from analytic signal, estimate f_inst(), the instantaneous
frequency
(4) look at the smoothed f_inst estimate, f_inst_smooth = filter(b,a,
f_inst)

The problem I have is that f_inst contains negative frequencies and I'm
not sure what to do with them-- help?

Thanks,
Marcus

in article 1140040868.355198.222480@z14g2000cwz.googlegroups.com,
magoldfish@gmail.com at magoldfish@gmail.com wrote on 02/15/2006 17:01:

> Just wondering how one practically handles negative frequencies
> obtained from estimating the instantaneous frequency using the Hilbert
> Transform.
> 
> Here is what I am doing:
> 
> (1) take a time series (e.g., speech phoneme or two), x
> (2) compute analytic signal, X = hilbert(x);
> (3) from analytic signal, estimate f_inst(), the instantaneous
> frequency
> (4) look at the smoothed f_inst estimate, f_inst_smooth = filter(b,a,
> f_inst)
> 
> The problem I have is that f_inst contains negative frequencies and I'm
> not sure what to do with them-- help?

if you visualize that analytic signal as a function of time, it might look
like a sorta cork-screw wrapping around the t-axis.  the rate that it wraps
around is the instantaneous frequency.  if the instantaneous frequency
changes signs, that means that the parametric curve that represents the
analytic signal has stopped wrapping in one direction or sense (say,
counter-clockwise) and has begun wrapping in the other direction (now
clockwise).

with only words that's about the only way i can illustrate it.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

What do you expect the instantaneous frequency of a speech signal to be
indicative of?

Dirk

"dbell" <dbell@niitek.com> writes:

> What do you expect the instantaneous frequency of a speech signal to be
> indicative of?

Coloured noise?

-- 
"And he sees the vision splendid 
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

 

You don't get any meaningful results by just computing analytic signal
and estimating instantaneous frequncy.

To get something meaningful you might have to do empirical mode
decomposition first, then compute analytic signal and instantaneous
frequency of each mode and finally arrive at the so called Hilbert
spectrum.

The whole methodology is called Hilbert-Huang Transform and it can be
found at
http://www.fuentek.com/technologies/hht.htm

I can think of easier ways to generate colored noise.

Dirk

Peter K. wrote:
> "dbell" <dbell@niitek.com> writes:
>
> > What do you expect the instantaneous frequency of a speech signal to be
> > indicative of?
>
> Coloured noise?
>
> --
> "And he sees the vision splendid
> of the sunlit plains extended
> And at night the wondrous glory of the everlasting stars."

dbell wrote:

> I can think of easier ways to generate colored noise.

Me too. :-)

Peter K. wrote:
> "dbell" <dbell@niitek.com> writes:
> 
> 
>>What do you expect the instantaneous frequency of a speech signal to be
>>indicative of?
> 
> 
> Coloured noise?

People who live in Hartford don't spell that way! ;)
> 

fizteh89 wrote:
> You don't get any meaningful results by just computing analytic signal
> and estimating instantaneous frequncy.
I agree with this statement for complex signals like speech, but what
about for simple fm signals/chirps?  Shouldn't the IF give me the
modulating signal?  This is the kind of information I am seeking.

> The whole methodology is called Hilbert-Huang Transform and it can be
Thanks for the pointer.  Already used the HHT-- seems very nice-- but
for the simple problem I am considering I think it is overkill: the
signal I am analyzing is not the sum of many AM-FM components, merely a
single AM-FM component.  Again, I expected the direct application of
the Hilbert transform + IA/IF estimation to be effective.

Has anyone actually used the Hilbert transform to estimate the IF of an
AM-FM signal + noise?  What do you practically do with the negative
frequencies it returns?

For a zero-mean FM signal I expect it to return the modulating
function.

Marcus