Update on Think DSP, and an explanation of the missing fundamental effect

On Tuesday, February 3, 2015 at 5:01:55 PM UTC-5, Rick Lyons wrote:
> On Wed, 28 Jan 2015 12:07:52 -0800 (PST), bellda2005@gmail.com wrote:
> 
>    [Snipped by Lyons]
> >
> >Hi Rick,
> >
> >You have actually run across the "missing fundamental" 1000's of times before. Every time you made a phone call on a land line the fundamental at a minimum was largely suppressed if not effectively eliminated (except maybe for squeaky children and extremely high-pitched people), yet you did not think the pitch was any different. The period of a waveform rich with harmonics will be unchanged whether the fundamental is present or not. That period is the pitch, is it not?
> >
> >An interesting question (not a proof of anything) is if the fundamental is missing for speech, what do you expect the pitch to be? It hasn't doubled because the waveform is not periodic in half the period of the fundamental. Some other choice?
> >
> >In mobile phones that use spectral coding bandwidth compression it would make sense to eliminate low frequencies including the fundamental to save bits, so I would guess it is probably done there, which could be more 1000s of times you have encountered it.
> >
> >Dirk
> >
> >Dirk Bell, MSEE, MSCF
> >Senior-Level DSP Engineer in search of a great opportunity.
> >Willing to relocate.
> >https://www.linkedin.com/in/dirkbell
> 
> Hi Dirk,
>    Your post is fascinating.  As I wrote, I don't 
> recall encountering this "missing fundamental effect" 
> before.  But now I realize that my past investigation of 
> audio "beat notes" is indeed an example of our 
> ear/brain mechanism hearing a "missing fundamental."
> 
> Then you, Dirk, come along and make the astounding claim 
> that our ability to hear "missing fundamental" tones is 
> necessary to explain how telephone systems work.  
>  
> And now I think you're correct, and here's why:
> I'm assuming that telephone systems filter out any 
> spoken audio energy below 300 Hz.  Next I generated an 
> audio tone of 250 Hz and played it through the speakers 
> of my desktop computer.  Listening to that tone I'm sure 
> the sound of my voice "sounds" much lower in frequency 
> than 250 Hz. (I cannot duplicate a tone as high as 250 Hz 
> with my voice.)
> 
> So if my voice sounds like it's spectral energy is less 
> than 250 Hz and telephone systems attenuate audio spectral 
> below 300 Hz, then how is it I'm able to call my brother and 
> complain about federal politicians over the telephone?
> 
> The only answer I can think of is that you're right Dirk. 
> The telephone system transmits *only* the harmonics of my 
> voice to my brother's house and my brother's ear/brain 
> mechanism somehow allows him to hear the low frequency 
> "missing fundamental" tones of my voice that were NOT 
> transmitted over the telephone system.
> 
> It all seems amazing to me, and I'm shocked* I haven't 
> heard about this subject before.
> 
> [-Rick-]
> * "Gambling! In Casablanca. I'm shocked."
>               -- Capt. Louis Renault

Hi Rick,

The thing about losing the fundamental is that the period (pitch) is UNCHANGED if there normal harmonics.  It appears to be the pitch you are hearing independent of whether there is any frequency component at the pitch frequency or not.

Dirk

bellda2005@gmail.com wrote:
> On Tuesday, February 3, 2015 at 5:01:55 PM UTC-5, Rick Lyons wrote:

(snip)

>> Then you, Dirk, come along and make the astounding claim 
>> that our ability to hear "missing fundamental" tones is 
>> necessary to explain how telephone systems work.  
  
(snip)

>> So if my voice sounds like it's spectral energy is less 
>> than 250 Hz and telephone systems attenuate audio spectral 
>> below 300 Hz, then how is it I'm able to call my brother and 
>> complain about federal politicians over the telephone?
 
(snip)

> The thing about losing the fundamental is that the period (pitch) 
> is UNCHANGED if there normal harmonics.  It appears to be the 
> pitch you are hearing independent of whether there is any 
> frequency component at the pitch frequency or not.

It should be possible to test this. Start with a signal with equal
amplitude 2nd and 3rd harmonics, and see if you hear the first.
Then slowly decrease the 2nd (or 3rd) and see at what point you
don't hear the 1st.

Remember that our brains are doing pattern matching to signals that
they have heard before. Many natural sounds have lots of harmonics.

I have wondered this more about cats. I think everyone with a cat 
knows that they learn the sound of a can opening, even if you rarely
feed them canned food. I doubt that they think about the harmonics
of a can or can opener, but match up the pattern.

Continuing the test, next try signals with 2nd, 4th and 5th, and see
at which amplitudes we hear, and don't hear, the 1st. 

We have to recognize sounds with similar, but not exact, harmonic
distribution as similar sounds, as there are too many things that 
naturally change the harmonics. But different enough, we have to
know that it is different.

-- glen

It would be interesting to mess around with the phases of the harmonics and see if that makes any difference. One theory of the missing fundamental principle is that you are sensitive to the modulation of the envelope of the signal (remember that the hair cells along the basilar membrane act as half-wave rectifiers). The envelope modulation would be affected by relative harmonic phase. 

Bob

On Tue, 3 Feb 2015 19:43:27 -0800 (PST), radams2000@gmail.com wrote:

>It would be interesting to mess around with the phases of the harmonics and=
> see if that makes any difference. One theory of the missing fundamental pr=
>inciple is that you are sensitive to the modulation of the envelope of the =
>signal (remember that the hair cells along the basilar membrane act as half=
>-wave rectifiers). The envelope modulation would be affected by relative ha=
>rmonic phase.=20
>
>Bob

Bob always brings these interesting insights that get down to the
fundamentals (ahem) of the issue.

I remember practical examples of this as a kid when radio speakers in
cars had to be small, so couldn't really physcially support the
wavelengths of the lower frequencies.   Music didn't sound horrible
(well, by the standards of the day, anyway), and the bass was still
there.   My understanding is that it was essentially the same effect.
The system filtered out the low end, but it didn't sound too awful or
not nearly as awful as one would have thought.


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

radams2000@gmail.com wrote:
> It would be interesting to mess around with the phases of the 
> harmonics and see if that makes any difference. One theory of 
> the missing fundamental principle is that you are sensitive to 
> the modulation of the envelope of the signal (remember that 
> the hair cells along the basilar membrane act as 
> half-wave rectifiers). The envelope modulation would 
> be affected by relative harmonic phase. 

Interesting.  As well as I know it (not so well) the signal is
processed two ways. One that uses phase differences to detect
the direction that sounds come from, and, separately, one that
uses frequencies and harmonics, but not phase, to give the musical
quality of the sound. 

-- glen

Since we are talking about perception,

Using headphones, play a 200 Hz tone in 1 ear and a 210 Hz tone in the other ear (you can use MATLAB), and see what happens. Use covered ear earphones if you have them so you are sure that there is no leakage from one earphone to the other ear. It is easy to explain the effect, but I don't know the reason for it.

If you really want to see something weird about perception, check out the McGurk Effect. (I may have posted this before, but it is worth another post.)

http://www.npr.org/blogs/krulwich/2011/09/23/140704746/whats-he-saying-bahh-or-fahh-a-brain-mystery 

Freaky.

On Wed, 28 Jan 2015 12:07:52 -0800 (PST), bellda2005@gmail.com wrote:

   [Snipped by Lyons]
>
>Hi Rick,
>
>You have actually run across the "missing fundamental" 1000's of times before. Every time you made a phone call on a land line the fundamental at a minimum was largely suppressed if not effectively eliminated (except maybe for squeaky children and extremely high-pitched people), yet you did not think the pitch was any different. The period of a waveform rich with harmonics will be unchanged whether the fundamental is present or not. That period is the pitch, is it not?
>
>An interesting question (not a proof of anything) is if the fundamental is missing for speech, what do you expect the pitch to be? It hasn't doubled because the waveform is not periodic in half the period of the fundamental. Some other choice?
>
>In mobile phones that use spectral coding bandwidth compression it would make sense to eliminate low frequencies including the fundamental to save bits, so I would guess it is probably done there, which could be more 1000s of times you have encountered it.
>
>Dirk
>
>Dirk Bell, MSEE, MSCF
>Senior-Level DSP Engineer in search of a great opportunity.
>Willing to relocate.
>https://www.linkedin.com/in/dirkbell

Hi Dirk,
   I ran two experiments:

**FIRST EXPERIMENT**:
Using Matlab software I generated a 600 Hz audio 
tone and played it through my desktop computer's 
speakers.

I used my TracPhone cell phone to call my home's 
landline phone number.

When my landline phone's answering machine started 
recording the incoming call I held my TracPhone up to 
my computer's speakers and recorded the 600 Hz tone 
on my landline's answering machine.

(So, ...that recorded 600 Hz tone has passed through 
my telephone company's system.)

I played the answering machine's audio 'message' and 
used a microphone to record that message (the 600 Hz 
tone) on my desktop computer.

Then I performed spectrum analysis (64K FFT size) of the 
microphone/PC recorded audio signal.  The spectral result 
was a "clean" 600 Hz tone with VERY low spectral 
background noise.

**SECOND EXPERIMENT**:
Next, using Matlab software I generated a 150 Hz audio 
tone and played it through my desktop computer's 
speakers.

I repeated the above steps calling my landline phone 
to record my answering machine's new audio message 
(now a 150 Hz tone sent through my telephone company's 
system) on my computer.

Again I performed spectrum analysis of the 
microphone/PC recorded audio signal.  The spectral result 
contained a moderate amount of spectral background noise, 
but there were two predominant spectral peaks.  Those 
peaks were at large-magnitude spectral peak at 450 Hz 
and peak at 600 Hz (roughly 12 dB down from the 450 Hz peak).

The spectrum contained no measureable energy at 150 Hz.

So there you have it: I could transmit a 600 Hz audio 
tone over my telephone system, but when I transmitted 
a 150 Hz tone all that arrived at my landline phone 
was the 2nd and 3rd harmonics (450 and 600 Hz) of the 
150 Hz tone.

Now here's the neat part: when I listened to my answering 
machine's "missing 150 Hz" audio it sounded like 
a 150 Hz tone to me!!

SOOooo, the telephone system does NOT work the way 
I thought it did.  It looks like the phone system 
doesn't transmit my audio voice signal, it only transmits 
the harmonics of my voice signal.  But the destination 
listener's ear/brain mechanism hears the "missing 
fundamental" spectral content of my voice.

As Al Clark would say, "You really 
can teach an old dog new tricks."  Ha ha.

[-Rick-]

On Tue, 3 Feb 2015 22:42:41 -0800 (PST),
bellda2005@gmail.com wrote:

>Since we are talking about perception,
>
>Using headphones, play a 200 Hz tone in 1 ear and a 210 Hz tone in the othe=
>r ear (you can use MATLAB), and see what happens. Use covered ear earphones=
> if you have them so you are sure that there is no leakage from one earphon=
>e to the other ear. It is easy to explain the effect, but I don't know the =
>reason for it.

See my discussion under the "Binaural Beats" subtopic at
<http://www.daqarta.com/dw_0obb.htm>.  Better yet, download
Daqarta and run the Beats_Demo mini-app.

Unlike conventional monaural beats, it's easy to see that
binaural beats *must* be happening entirely in the brain.
If you listen carefully, you note that it doesn't really
sound like monaural beats.... more like a single source is
rotating around your head.  (Try a slower frequency, like 1
Hz, to make this clearer.)  In fact, this effect is just
what you'd get from the rotating source, as the phase
difference between the signals at the two ears is
continually changing.

Note that "binaual beats" has become a darling of the
woo-woo set, typically with the "beat" rate set to match
some brain wave frequency.

I'd like to encourage everyone to try a 300 Hz center
frequency with 1 Hz difference.  For me, it causes my middle
ear muscles to contract at the beat rate... big "thump,
thump" sounds, *very* disconcerting!  See the
"Middle Ear Thumping" section under the above link.

Best regards,





>If you really want to see something weird about perception, check out the M=
>cGurk Effect. (I may have posted this before, but it is worth another post.=
>)
>
>http://www.npr.org/blogs/krulwich/2011/09/23/140704746/whats-he-saying-bahh=
>-or-fahh-a-brain-mystery=20
>
>Freaky.

Bob Masta
 
              DAQARTA  v7.60
   Data AcQuisition And Real-Time Analysis
              www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
 Frequency Counter, Pitch Track, Pitch-to-MIDI 
   FREE Signal Generator, DaqMusiq generator    
          Science with your sound card!

On Wednesday, February 4, 2015 at 1:42:44 AM UTC-5, belld...@gmail.com wrote:
> Since we are talking about perception,
> 
> Using headphones, play a 200 Hz tone in 1 ear and a 210 Hz tone in the other ear (you can use MATLAB), and see what happens. Use covered ear earphones if you have them so you are sure that there is no leakage from one earphone to the other ear. It is easy to explain the effect, but I don't know the reason for it.
> 
> If you really want to see something weird about perception, check out the McGurk Effect. (I may have posted this before, but it is worth another post.)
> 
> http://www.npr.org/blogs/krulwich/2011/09/23/140704746/whats-he-saying-bahh-or-fahh-a-brain-mystery 
> 
> Freaky.


Although unrelated to audio transmission, it is related to audio perception and the link to video perception. It's the McGurk effect - I hadn't heard of this before. It's best if I don't explain it - for those that want to experience it for themselves - it fooled me the first time (and several times after).

Here's a youtube link: https://www.youtube.com/watch?v=G-lN8vWm3m0

Cheers,
David

On Wednesday, February 4, 2015 at 6:54:45 AM UTC-5, Rick Lyons wrote:
> On Wed, 28 Jan 2015 12:07:52 -0800 (PST), bellda2005@gmail.com wrote:
> 
>    [Snipped by Lyons]
> >
> >Hi Rick,
> >
> >You have actually run across the "missing fundamental" 1000's of times before. Every time you made a phone call on a land line the fundamental at a minimum was largely suppressed if not effectively eliminated (except maybe for squeaky children and extremely high-pitched people), yet you did not think the pitch was any different. The period of a waveform rich with harmonics will be unchanged whether the fundamental is present or not. That period is the pitch, is it not?
> >
> >An interesting question (not a proof of anything) is if the fundamental is missing for speech, what do you expect the pitch to be? It hasn't doubled because the waveform is not periodic in half the period of the fundamental. Some other choice?
> >
> >In mobile phones that use spectral coding bandwidth compression it would make sense to eliminate low frequencies including the fundamental to save bits, so I would guess it is probably done there, which could be more 1000s of times you have encountered it.
> >
> >Dirk
> >
> >Dirk Bell, MSEE, MSCF
> >Senior-Level DSP Engineer in search of a great opportunity.
> >Willing to relocate.
> >https://www.linkedin.com/in/dirkbell
> 
> Hi Dirk,
>    I ran two experiments:
> 
> **FIRST EXPERIMENT**:
> Using Matlab software I generated a 600 Hz audio 
> tone and played it through my desktop computer's 
> speakers.
> 
> I used my TracPhone cell phone to call my home's 
> landline phone number.
> 
> When my landline phone's answering machine started 
> recording the incoming call I held my TracPhone up to 
> my computer's speakers and recorded the 600 Hz tone 
> on my landline's answering machine.
> 
> (So, ...that recorded 600 Hz tone has passed through 
> my telephone company's system.)
> 
> I played the answering machine's audio 'message' and 
> used a microphone to record that message (the 600 Hz 
> tone) on my desktop computer.
> 
> Then I performed spectrum analysis (64K FFT size) of the 
> microphone/PC recorded audio signal.  The spectral result 
> was a "clean" 600 Hz tone with VERY low spectral 
> background noise.
> 
> **SECOND EXPERIMENT**:
> Next, using Matlab software I generated a 150 Hz audio 
> tone and played it through my desktop computer's 
> speakers.
> 
> I repeated the above steps calling my landline phone 
> to record my answering machine's new audio message 
> (now a 150 Hz tone sent through my telephone company's 
> system) on my computer.
> 
> Again I performed spectrum analysis of the 
> microphone/PC recorded audio signal.  The spectral result 
> contained a moderate amount of spectral background noise, 
> but there were two predominant spectral peaks.  Those 
> peaks were at large-magnitude spectral peak at 450 Hz 
> and peak at 600 Hz (roughly 12 dB down from the 450 Hz peak).
> 
> The spectrum contained no measureable energy at 150 Hz.
> 
> So there you have it: I could transmit a 600 Hz audio 
> tone over my telephone system, but when I transmitted 
> a 150 Hz tone all that arrived at my landline phone 
> was the 2nd and 3rd harmonics (450 and 600 Hz) of the 
> 150 Hz tone.
> 
> Now here's the neat part: when I listened to my answering 
> machine's "missing 150 Hz" audio it sounded like 
> a 150 Hz tone to me!!
> 
> SOOooo, the telephone system does NOT work the way 
> I thought it did.  It looks like the phone system 
> doesn't transmit my audio voice signal, it only transmits 
> the harmonics of my voice signal.  But the destination 
> listener's ear/brain mechanism hears the "missing 
> fundamental" spectral content of my voice.
> 
> As Al Clark would say, "You really 
> can teach an old dog new tricks."  Ha ha.
> 
> [-Rick-]

Hi Rick,

With the 150 Hz tone, you had distortion in the processing chain generating the harmonics.  It could have been a) your signal generation process (might be some from poor resampling if that happens, maybe some from your speakers), b) your transmission process (probably VoIP land line which has audio coding/decoding), c) your recording process (your answering machine probably has coding/decoding if it is digital) or d) some combination of a) - c).  It would have to happen before the band limiting took place. So you generated a third harmonic at 450 Hz and a fourth harmonic at 600 Hz. I suspect that there are other harmonics also. If it were not for the distortion, assuming the same high-pass filter, you would have recorded something very low level or essentially nothing at all.  The harmonics from the distortion establish the period of the waveform corresponding to the original frequency making it sound like you recorded the original tone. 

This is different from speech which has the harmonics present when generated.

Dirk