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

Started by AllenDowney January 21, 2015
Last week I posted blog article on Chapter 4 of Think DSP, which is about
noise:

http://thinkdsp.blogspot.com/2015/01/think-dsp-chapter-4-noise.html

The article includes this notebook, where I present the missing fundamental
effect, where we hear a low pitch even if the signal contains no power at
that frequency:

http://nbviewer.ipython.org/github/AllenDowney/ThinkDSP/blob/master/code/saxophone.ipynb

This week I posted Chapter 5, which is about autocorrelation

http://thinkdsp.blogspot.com/2015/01/think-dsp-chapter-5-autocorrelation.html

The article includes this notebook, which uses autocorrelation to crack the
case of the missing fundamental:

http://nbviewer.ipython.org/github/AllenDowney/ThinkDSP/blob/master/code/saxophone2.ipynb

As always, comments from Comp.DSP are welcome (but let's try not to get
bogged down on the plural of spectrum :)	 

_____________________________		
Posted through www.DSPRelated.com
This effect is the basis for bass extension algorithms where you create harmonics to get fake bass from small speakers. But my experience is that it doesn't work so well. What happens when the input signal is not a solo instrument with a periodic waveform? Then it just makes a mess of things. Commercial bass-boost algorithms combine harmonic generation with old-fashioned dynamic bass boost to handle the non-harmonic cases like a kick drum. But they don't mention this in their advertising. 

Regarding the mechanism for how the ear perceives the missing fundamental, I don't believe that there is any explicit autocorrelation mechanism. A more likely explanation is the modulation of the envelope of the signal which will occur at the fundamental frequency even if the fundamental is not present. 

Bob 
On Wed, 21 Jan 2015 09:52:00 -0800, radams2000 wrote:

> This effect is the basis for bass extension algorithms where you create > harmonics to get fake bass from small speakers. But my experience is > that it doesn't work so well. What happens when the input signal is not > a solo instrument with a periodic waveform? Then it just makes a mess of > things. Commercial bass-boost algorithms combine harmonic generation > with old-fashioned dynamic bass boost to handle the non-harmonic cases > like a kick drum. But they don't mention this in their advertising. > > Regarding the mechanism for how the ear perceives the missing > fundamental, I don't believe that there is any explicit autocorrelation > mechanism. A more likely explanation is the modulation of the envelope > of the signal which will occur at the fundamental frequency even if the > fundamental is not present. > > Bob
Not an autocorrelation function as such, since the ears sense sound in a sort of combination frequency/time manner (oooh! Wavelets!). The ear senses sound with something like a massive bank of filters ("hair cells", which are embedded in the cochlea, which has a definite frequency/ distance dependence). If you grow up in an environment where sounds tend to have lots of overtones, your brain will naturally tend to correlate f, 2f, 3f, etc. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Tim Wescott <seemywebsite@myfooter.really> wrote:
> On Wed, 21 Jan 2015 09:52:00 -0800, radams2000 wrote:
>> This effect is the basis for bass extension algorithms where you create >> harmonics to get fake bass from small speakers. But my experience is >> that it doesn't work so well.
(snip)
> Not an autocorrelation function as such, since the ears sense sound in a > sort of combination frequency/time manner (oooh! Wavelets!).
> The ear senses sound with something like a massive bank of filters ("hair > cells", which are embedded in the cochlea, which has a definite frequency/ > distance dependence). If you grow up in an environment where sounds tend > to have lots of overtones, your brain will naturally tend to correlate f, > 2f, 3f, etc.
Some years ago I had a book that included a floppy-ROM (also known as an analog audio recording) with stretched octaves. They made musical sounds that used 2.1x instead of 2x for an octave, and of course they sounded very non-musical. The experiment they didn't do (for a good reason) was to raise babies so that they only heard stretched octaves. The neural connections would form differently. Similarly, as far as I know they way our brains learn to figure out color vision is through the correlations in the signals coming in. If babies were raised in a colorless environment, they might not learn how to decode colors. It might be that the feeling each of us feels when we see a color depends on how the wiring was done when we were young. That is, on the first colors that we saw, and how we saw them. But again, an experiment not likely to be done. -- glen
On Wed, 21 Jan 2015 19:33:56 +0000, glen herrmannsfeldt wrote:

> Tim Wescott <seemywebsite@myfooter.really> wrote: >> On Wed, 21 Jan 2015 09:52:00 -0800, radams2000 wrote: > >>> This effect is the basis for bass extension algorithms where you >>> create harmonics to get fake bass from small speakers. But my >>> experience is that it doesn't work so well. > > (snip) >> Not an autocorrelation function as such, since the ears sense sound in >> a sort of combination frequency/time manner (oooh! Wavelets!). > >> The ear senses sound with something like a massive bank of filters >> ("hair cells", which are embedded in the cochlea, which has a definite >> frequency/ >> distance dependence). If you grow up in an environment where sounds >> tend to have lots of overtones, your brain will naturally tend to >> correlate f, 2f, 3f, etc. > > > Some years ago I had a book that included a floppy-ROM (also known as an > analog audio recording) with stretched octaves. > > They made musical sounds that used 2.1x instead of 2x for an octave, and > of course they sounded very non-musical. > > The experiment they didn't do (for a good reason) was to raise babies so > that they only heard stretched octaves. The neural connections would > form differently. > > Similarly, as far as I know they way our brains learn to figure out > color vision is through the correlations in the signals coming in. If > babies were raised in a colorless environment, they might not learn how > to decode colors. > > It might be that the feeling each of us feels when we see a color > depends on how the wiring was done when we were young. That is, on the > first colors that we saw, and how we saw them. But again, an experiment > not likely to be done.
Kittens raised in an environment that has no visible edges cannot, after a certain age, ever learn to see edges. So it's similar. You could maybe do the sound experiment with songbirds, then analyze what comes out when they grow up. It'd be hard, though, since one hears the sounds one produces, and those have harmonically related overtones. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
On 1/21/2015 8:29 AM, AllenDowney wrote:
> Last week I posted blog article on Chapter 4 of Think DSP, which is about > noise: > > http://thinkdsp.blogspot.com/2015/01/think-dsp-chapter-4-noise.html >
Allen: Your opus rocks!! I am learning and installing Python just so I can run your examples. Congrats and thanks. -Ramon
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Allen:

Please find attached a noise that is the bane of my existence, my 
"Ahab's Whale".

The sample includes the breath of the speaker (who *did* inhale), and it 
comes from here:

https://www.youtube.com/watch?v=Aju752l0tP4
(the noise starts at minute 1 and goes all the way to the end)

Feel free to add a chapter on how to remove it.   ;-)

TIA,

-Ramon




On 1/21/2015 8:29 AM, AllenDowney wrote:
> Last week I posted blog article on Chapter 4 of Think DSP, which is about > noise: > > http://thinkdsp.blogspot.com/2015/01/think-dsp-chapter-4-noise.html >
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On Wed, 21 Jan 2015 09:52:00 -0800 (PST),
radams2000@gmail.com wrote:

>This effect is the basis for bass extension algorithms where you create har= >monics to get fake bass from small speakers. But my experience is that it d= >oesn't work so well. What happens when the input signal is not a solo instr= >ument with a periodic waveform? Then it just makes a mess of things. Commer= >cial bass-boost algorithms combine harmonic generation with old-fashioned d= >ynamic bass boost to handle the non-harmonic cases like a kick drum. But th= >ey don't mention this in their advertising.=20 > >Regarding the mechanism for how the ear perceives the missing fundamental, = >I don't believe that there is any explicit autocorrelation mechanism. A mor= >e likely explanation is the modulation of the envelope of the signal which = >will occur at the fundamental frequency even if the fundamental is not pres= >ent.=20
I've long suspected this was the explanation. When you look at a "missing fundamental" waveform on a scope, the periodicity at the (missing) fundamental is very obvious. With 0-phase harmonics you see one cycle of a big sinusoid (of roughly the highest component frequency) which repeats at the missing fundamental frequency. Between those peaks are lower-level ripples. All it would take is a nonlinearity in the ear to convert the "missing" fundamental into a real tone. However, when I mentioned this to some of the guys in the hearing research lab where I used to work, they assured me that others had investigated this and ruled it out. I don't recall the exact experiment, but I *think* it was something like an attempt to cancel the "missing" fundamental with an out-of-phase sine wave. I do recall that I was never really convinced. As Tim mentions, the ear deconstructs the incoming sound to component frequencies via the equivalent (for this discussion anyway) of a bank of filters. Each filter's output is a pulse train of neural spikes at a rate proportional to the amplitude of its "characteristic frequency". The pulse rate is very low, typically a few hundred Hz. An important point, which many folks have a hard time keeping in mind, is that in general there is no real "frequency content" in neural firing rates...they encode *amplitude* of their characteristic frequency. The system encodes audio frequency by the position of the active fibers across the whole set, not the signal on any single fiber. (Just like bank of filters with rectified-and-filtered outputs, each feeding a VCO whose pulse rate varies with amplitude.) However, even though the pulses can't follow the characteristic frequency, they tend to synchronize to it such that the neuron is more likely to fire on a peak of the component when it does fire, after which it may remain in a "refactory" state for multiple cycles until it fires again. This is all statistical, not a hard lock, but it is very clear in a time histogram of spike firings. The parallel bundle of neurons, each carrying its own spike train for its own characteristic frequency, then proceed out to the cochlear nucleus and on up to higher brain centers. Any sort of correlation (or envelope detection) would then have to be performed by summation of spike trains from multiple neurons onto an intermediate neuron, again all statistical... if enough spikes arrive within a small-enough time window such that their (weighted) sum exceeds the firing threshold for that neuron, then it fires. The cochlear nucleus contains lots of intermediate neurons doing all sorts of combination tricks as a preliminary stage of auditory processing, before handing things off to the higher brain centers. There may be simple ways to recover a missing fundamental that could be done right there. I've failed to keep up with the field, however, so I don't know the current thinking. 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 1/22/2015 8:42 AM, AllenDowney wrote:
> This is an interesting, and annoying, noise! I will pass this along as an > option for the students to explore and let you know if we find anything > useful. > > Thanks for all the comments on this thread -- there is a lot of good > stuff! > > Allen >
Professor Downey: I will post something like a 1-minute, 4-minute and the full audio in some Internet file service (DropBox, etc.) For those who are not aware: you can take a file with human voice plus noise and use several packages which *attempt* to repair (denoise) it. The obvious solution is to remove *stuff* from it. That process is not unlike that performed by a cancer surgeon: what exactly to remove and what to leave in?? The problem is that of false positives and false negatives: (a) Sometimes you (and/or the software app) are not aggressive enough. Too much of the noise remains, but at least the human sounds like a human. (b) Sometimes you go overboard. All the noise is removed and then some! The person's voice sounds unnatural. This sound is variously known as "wine glass" or "metallic bubbles". See my thread: "The 3 Interactive Ways to Perform Noise Reduction/Removal" in this NG. A 4th. way was discovered. Thanks again for helping me capture my "Moby Dick". -Ramon "Captain Ahab" Herrera http://en.wikipedia.org/wiki/Captain_Ahab_%28Moby-Dick%29