instantaneous frequency wiht Hilbert transform?

On Fri, 17 Feb 2006 03:16:11 GMT, R.Lyons@_BOGUS_ieee.org (Rick Lyons)
wrote:


>
>Hi Andrew,
>
>  I've modeled that "instantaneous frequency" 
>computation scheme for triangular time sequences 
>that have a "fundamental plus harmonics"
>spectral content.  The scheme seems to work 
>fine sl long as the differentiator has a sufficiently 
>wideband frequency range of operation.
>
>Maybe, when I have a chance, I should experiment with 
>that FM demod scheme against actual speech signals.
>
>See Ya',
>[-Rick-]

Andrew,

  you "stuck a burr under my saddle" ...
as normal heterosexual cowboys would say.

I did a little additional MATLAB modeling using 
speech signals from ".wav" files
of the FM demod method:

  * compute the analytic (complex) version 
    of a FM signal located 
    at some non-zero carrier frequency;

  * translate that analytic signal down 
    to zero Hz (baseband);

  * compute the instantaneous phase angle of the 
    baseband analytic signal;

  * differentiate that instantaneous phase angle
    sequence to obtain the modulating signal that
    was used to create the orignal FM signal.

The entire scheme does work properly to obtain 
the original modulating signal.  The modulation 
index has, as you probably already know, a  
profound impact of the entire process.

It looks like very simple (first-difference and 
central-difference) differentiators are indeed quite 
useful for performing digitial differentiation
in my modeling.   My sample rate was 11025 Hz.

Some of the audio ".wav" files that I used as 
modulation for my simulated FM signals seemed 
to provide "better" FM demod output than 
other audio files.  Further study, by me, is needed.

In any case, the whole process seems to work 
darned well.

I wanted to use some Capt. Kirk ".wav" audio 
files that I found on the Internet, but MATLAB couldn't 
read those audio files.  DARN IT !!   I had to settle for 
Mr.T audio files ("I pity the fool that messes with me")

[-Rick-]
 

Rick Lyons wrote:

> Andrew,
>
>   you "stuck a burr under my saddle" ...
> as normal heterosexual cowboys would say.

:-)

geez, i guess i better hurry and see Brokeback to see the size of those
guys' burrs.  i hope their names aren't Andrew or Rick.  actually
"Munich" is the one i've been intending on seeing if we can get someone
to watch the kids.

r b-j

"robert bristow-johnson" <rbj@audioimagination.com> writes:

> Rick Lyons wrote:
> 
> >   you "stuck a burr under my saddle" ...
> > as normal heterosexual cowboys would say.
> 
> :-)
> 
> geez, i guess i better hurry and see Brokeback to see the size of those
> guys' burrs.  i hope their names aren't Andrew or Rick. 

http://www.youtube.com/watch?v=zfODSPIYwpQ

Ciao,

Peter K.

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

 

Hi Rick,

On Sat, 18 Feb 2006 02:39:37 +0000, Rick Lyons wrote:

> On Fri, 17 Feb 2006 03:16:11 GMT, R.Lyons@_BOGUS_ieee.org (Rick Lyons)
> wrote:
> 
> 
> 
>>Hi Andrew,
>>
>>  I've modeled that "instantaneous frequency"
>>computation scheme for triangular time sequences that have a "fundamental
>>plus harmonics" spectral content.  The scheme seems to work fine sl long
>>as the differentiator has a sufficiently wideband frequency range of
>>operation.
>>
>>Maybe, when I have a chance, I should experiment with that FM demod
>>scheme against actual speech signals.
>>
>>See Ya',
>>[-Rick-]
> 
> Andrew,
> 
>   you "stuck a burr under my saddle" ...
> as normal heterosexual cowboys would say.
> 
> I did a little additional MATLAB modeling using speech signals from ".wav"
> files
> of the FM demod method:
> 
>   * compute the analytic (complex) version
>     of a FM signal located
>     at some non-zero carrier frequency;

Hold it right there, (pardner!)

As soon as you do the FM modulation thing, (apart from at very odd
modulation indices), you've already built a signal that essentially has
only one sensible "instantaneous frequency", and so phase differentiation
should work OK to decode it.  (And, as you say, it does.)  (If you squint
at it right, and don't think too hard about what "frequency" means, in
that context.)

The situation that I thought that I was replying to, though, was that of
just feeding a speech signal into an "analytic signal phase
differentiation engine", and expecting something useful, like frequency of
vocal fundamental, or the more musical notion of "pitch" to come out of
it.  Neither of those work very well. (Pitch is particularly prolematical,
as I'm sure you know.)

>   * translate that analytic signal down
>     to zero Hz (baseband);
> 
>   * compute the instantaneous phase angle of the
>     baseband analytic signal;
> 
>   * differentiate that instantaneous phase angle
>     sequence to obtain the modulating signal that was used to create the
>     orignal FM signal.
> 
> The entire scheme does work properly to obtain the original modulating
> signal.  The modulation index has, as you probably already know, a
> profound impact of the entire process.
> 
> It looks like very simple (first-difference and central-difference)
> differentiators are indeed quite useful for performing digitial
> differentiation in my modeling.   My sample rate was 11025 Hz.
> 
> Some of the audio ".wav" files that I used as modulation for my
> simulated FM signals seemed to provide "better" FM demod output than
> other audio files.  Further study, by me, is needed.
> 
> In any case, the whole process seems to work darned well.
> 
> I wanted to use some Capt. Kirk ".wav" audio files that I found on the
> Internet, but MATLAB couldn't read those audio files.  DARN IT !!   I
> had to settle for Mr.T audio files ("I pity the fool that messes with
> me")
> 
> [-Rick-]

Sorry for giving you a bum steer (or alluding to one  :-)

Cheers,

-- 
Andrew

On 17 Feb 2006 18:24:37 -0800, "robert bristow-johnson"
<rbj@audioimagination.com> wrote:

>
>Rick Lyons wrote:
>
>> Andrew,
>>
>>   you "stuck a burr under my saddle" ...
>> as normal heterosexual cowboys would say.
>
>:-)
>
>geez, i guess i better hurry and see Brokeback to see the size of those
>guys' burrs.  i hope their names aren't Andrew or Rick.  actually
>"Munich" is the one i've been intending on seeing if we can get someone
>to watch the kids.
>
>r b-j

  Ha ha.

   Your' movie tolerance is greater than mine. 
I don't wanna see two sheep herders ridin' each 
other bareback.

I'd rather see Sylvester Stallone rippin' off 
the arms and legs of the bad guys.

[-Rick-]
 

On Mon, 20 Feb 2006 01:02:22 +1100, Andrew Reilly
<andrew-newspost@areilly.bpc-users.org> wrote:

>Hi Rick,
>
  (snipped)
>
>Sorry for giving you a bum steer (or alluding to one  :-)
>
>Cheers,

Hi Andrew,

   Ha, ... you didn't.  You made me learn.


       Cowboy quote:

         "Don't squat with your spurs on."

[-Rick-]

Rick Lyons wrote:
>
>   Ha ha.
>
>   Your movie tolerance is greater than mine.

actually, i hardly ever see first run movies except ones we can take
the girls to (getting child care outside of school is a female canine).
 last one was Narnia.

what i really wanna see is movies that indulge my political POV like i
think Munich might.

> I don't wanna see two sheep herders ridin' each other bareback.
>
> I'd rather see Sylvester Stallone rippin' off the arms and legs of the bad guys.

i just got done seeing the Governator committing some really explicit
misogynic acts of violence on some cyborg bitch on broadcast TV (CBS or
whoever channel 3 is here).

geez, american hollywood is so creative. i just can't tell the
difference between Sylvester Schwarzenegger or Claude Stallone or that
Arnold vanDamn guy.  what's the big deel?  well, at least they can't be
riding each other (and you never see their "burrs", and only a couple
of times their "saddles"), but if they ever put these guys in the same
movie, who knows?  could get a lot of ratings.

say, Rick (or any other folks on the Left Coast), how's that Governator
doing?  ain't you glad you ditched that Gray Davis and replaced him
with
http://politicalhumor.about.com/library/images/blpic-arnoldgovernator.htm
?

r b-j