1/f (pink noise) generator in the ELF band

[Tony Stewart]

i found the audio spectrum in the MM5587 using an 8 channel Yamaha spectrum equalizer varied too much for my liking every few seconds which is why I said it was only good for audio above 1Hz with some 0.3Hz modulation in each channel.

Edit ,
I am having 2nd thoughts about your spectrum with how many spectral decades you need.
Do you need the impulse interval over 5 decades or just 2 or 3 decades with harmonics limited to 100Hz? If so the synthesis will be different. Weighted Random periods of impulses between f1 and f2 or a much smaller range of 2 decades with harmonics for the top few decades.

Averaged over time, longer than the lowest frequency, the average random spectrum may be the same, but over the short term may be quite different. As you know an theoretical impulse has an infinite bandwidth and practical ones limited by the pulse width, T have recursive notches in spectrum starting at 1/T then 1/2T,1/3T... 1/nT as the spectral envelopes reducing in amplitude with 1/n but relative flat like white noise up to 1/2 f the clock rate.

In the end you need to define if more than 2 or more random impulse generator with input clocks and attenuation spaced by decades OR just 1 random impulse generator with a shift length of n bits has the longest flicker interval at 1000 seconds with impulse harmonics band limited to 100Hz and a random sequence up 1/2 the clock rate but in a random pattern that cycles in 2^n counts, or 64K cycles for a 32bit generator.

 

[researcher]

Dear All,

I really thank for everybody for this huge effort to try to solve this not easy problem. I appreciated that.
I understood that generating such a low frequency signals is highly challenging in terms of circuit construction.

The scientific study what I want to reproduce is almost 20 years old and the authors somehow solved the problem to generate ULF 1/f noise, so perhaps I misunderstood the original description of the experimental device.
There was only 2 lines about the specifications of the 1/f generator:

"The set of generators enabled us to chose signals of any of four types - a random signal with a 1/f spectrum, a random signal with white noise spectrum and periodic signals. The spectral power density of the fluctuations of the 1/f signal and the of the white noise signal was concentrated in the frequency range 0.001 - 10Hz"

So how do you interpret these things?

I really thank to OBW0549 the schematic, this is exactly I am looking for, because this generator use the "natural" 1/f noise of an OPAMP and not an artificial "pinkified" white noise.

Somebody mentioned the DC response amplifier. This seems to me a very useful device for my project, because I would like to drive some coils using the pink noise.
Can anybody provide me a real schematic about this kind of amplifier?
Thank you in advance!

G.

 

[JimB]

The spectral power density of the fluctuations of the 1/f signal and the of the white noise signal was concentrated in the frequency range 0.001 - 10Hz"

The cynic (realist) in me says that they just used fairly loosely defined "low frequency noise", it could also be that the first draft of the report said <frequency range DC to 10Hz>.
As DC is not really a "frequency", it was edited in the second draft to 0.001Hz to infer a "very low frequency".

Unless you could track down someone associated the original study and ask them, you will probably never know.

JimB

 

[dr pepper]

Hi.
How about a power op amp?
Heres a datasheet for a lm675, on the first page theres a x20 non inverting amp dc coupled, looks like its good for 3 amps down to dc, at low freq you'll need a extra large heatsink, double is a good start.

 

[AnalogKid]

I really thank to OBW0549 the schematic, this is exactly I am looking for, because this generator use the "natural" 1/f noise of an OPAMP and not an artificial "pinkified" white noise.

Again, the mathematics of noise are very well understood. Assuming these three options all use rigorous circuit design techniques, ""natural" 1/f noise", ""pinkified" white noise", and a lookup table driving a D/A converter are the.same.thing. I suspect I know why the word "natural" keeps popping up, but that does not change the fizix.

ak

 

[researcher]

Again, the mathematics of noise are very well understood. Assuming these three options all use rigorous circuit design techniques, ""natural" 1/f noise", ""pinkified" white noise", and a lookup table driving a D/A converter are the.same.thing. I suspect I know why the word "natural" keeps popping up, but that does not change the fizix.

ak

Let me a little bit more precise: The mathematics of white noise is very well understood.
However the reality is that the origin of the pink noise is still not clear. There are just competing theories about it, there is no real consensus, and according to many serious scientist, the pink noise is still a mystery, a real enigma.
There is a relatively good summary about it:
1/f noise - a pedagogical review

The most widely accepted theory about the origin of the pink noise is the self-organised criticality (SOC) by Bak, Tang and Wiesenfeld.

I understand that for an engineer a noise (pink or white) is nothing more than an annoying thing what should have been eliminated from a circuit, but for a biologist the 1/f fluctuations of the biological systems is the real essence of the living state. Any difference in the pink noise spectra of a living organism means some kind of pathological state. (and cancer is the best example for that) This statement is the basic principle of the so called "fractal physiology". (https://www.worldscientific.com/worldscibooks/10.1142/8577)

In the biologist's point of wiev, the "pinkified white noise" is absolutely not equal with a real pink noise.

G.

 

[AnalogKid]

However the reality is that the origin of the pink noise is still not clear. There are just competing theories about it, there is no real consensus, and according to many serious scientist, the pink noise is still a mystery, a real enigma.

Which has nothing to do with what I said. I am familiar with the origins of the nature of pink noise. But *why* it occurs in nature has nothing to do with its definition, and that is firmly established in many places, including your first post.

I understand that for an engineer a noise (pink or white) is nothing more than an annoying thing what should have been eliminated from a circuit,

Then I suggest that you expand your "understanding" beyond myopic and ill-conceived opinions.

Any difference in the pink noise spectra of a living organism...

"What we have here is a failure to communicate." Pink noise is a rigidly defined concept. If the spectra of pink noise deviates, then it no longer is pink noise. A better way to make your statement is to say that the noise spectra of a living organism can deviate from pink. This is the same way an audio amplifier or speaker or listening room can alter pink noise spectra to something that is not pink, revealing attributes about their design and construction. OBTW, that is just one example of how an "engineer' might intentionally create noise for a useful purpose.

In the biologist's point of wiev, the "pinkified white noise" is absolutely not equal with a real pink noise.

I submit that that is because you are re-defining or misapplying a term that is well understood across multiple disciplines.

My pedigree: After my pro audio/video life and before my MIL-rugged life I spent a decade (full and part time) designing and building equipment for university research (Psychology, Chemistry, medical, speech and hearing, education, marketing, etc.). Among other things, I created and manipulated electrical, acoustic, visual, and tactile noise as needed.

ak

 

[alec_t]

However the reality is that the origin of the pink noise is still not clear. There are just competing theories about it,

I have absolutely no prior experience in the biological aspects of pink noise, but as a physicist let me add my own theory to the mix :-
All objects, be they cells or molecules or whatever, have mass. It takes less energy to move/vibrate a mass at low speeds/frequencies than at high speeds/frequencies. Therefore there is a greater tendency for low frequency events than high frequency events. Hence a 1/f factor. Given that events in nature are predominantly random, this leads to an overall 1/f pink noise distribution of events.

 

[Tony Stewart]

My experience here is related to clean room particle counts and high voltage Distribution transformers.

The quantity of dust particles is inverse to the size of the particles fairly consistently per unit volume (for most dust types). I have measured with laser particle counters with 16 channel histograms for Clean rooms of Class 100, 10k and outside, with office levels up to 1 million/cu.ft. when smoking was permitted with lots of dust. Breakdown voltage is a function of material type and gap size, so in an electric field, one would expect smaller particles to contribute towards lower energy discharges aand larger particles to create more energy less frequently giving the 1/f flicker type noise.

When charge carriers in a fluid insulator ( dielectric) are energized by some external electric field, a breakdown voltage (BDV) is gap related , in V/um and if these particles become the charge carriers then the rate of voltage rise and frequency of discharging both increase as size is reduced. I expected this would appear like like pink noise as energy vs frequency is plotted by some slope of 1/f. But it did not.

In this case, I was testing HV transformer with a rating of 5MVA from 10kV to 100kV and at some threshold a very repeatable 1 minute cycle of discharge could be measured as the frequency of constant PD "ticks" increased with excitation voltage like a Relaxation Oscillator but with a quadratic response above some threshold. So this was not like Pink Noise so I hypothesized the energy level for electron emission was constant and independent of particle size, so smaller sized particles must have clustered together to become large 1 particle of a similar size, thus giving a constant Partial breakdown voltage within the medium.

 

[AnalogKid]

"
(In this case, I used very pure transformer insulating oil contaminated with invisible but finite amount of cold-rolled-grain-oriented-silicon steel laminate dust.)
"

You are having WAY more fun at work than I am.

ak

 

[Tony Stewart]

It was fun and a million dollar liability problem with epidemic failures. All caused by a somewhat random but repetitive rate of 10 watt detonations creating an accelerated rate concentration of hydrogen in oil until early yank out of service. Although not as slow as 0.001 Hz, more like 0.01 Hz to 500 Hz but spanning up my measurement resolution <1ns rise time.

 

[researcher]

Hi.
How about a power op amp?
Heres a datasheet for a lm675, on the first page theres a x20 non inverting amp dc coupled, looks like its good for 3 amps down to dc, at low freq you'll need a extra large heatsink, double is a good start.

Thank you very much. This is a very good idea, I will try.

 

[researcher]

My pedigree: After my pro audio/video life and before my MIL-rugged life I spent a decade (full and part time) designing and building equipment for university research (Psychology, Chemistry, medical, speech and hearing, education, marketing, etc.). Among other things, I created and manipulated electrical, acoustic, visual, and tactile noise as needed.

ak[/QUOTE]

I really appreciate your expertise. If you are very familiar in noise generating apparatuses please help me to design one which fulfill those requirements what I quoted from the original research paper. I thank you for the technical explanations but I can do anything only with a schematic, as I wrote at the beginning, I can not design a circuit, but I can build it according to a proper plan.

Thanks in advance.

G.

 

[researcher]

Unless you could track down someone associated the original study and ask them, you will probably never know.

JimB

I am afraid, you are right...

 

[researcher]

Nobody has any more idea or suggestion?

 

[Tony Stewart]

Well, this "internal structure" of the pink noise is the real point in the 1/f fluctuations. (at least for a biologist)

I think you know if you make a FFT analysis on a music (for example a Mozart sonata) you will get the perfect 1/f power spectral density. And you will got the same thing if you analyse in the same way a Chopin concerto, however the two music can be distinguish easily, because the internal structures are different but looks exactly the same after spectral analysis.
This internal structure of the pink noise is come from (...well nobody knows exactly from where...) the so called self organised criticality. The real pink noise has a fractal structure, has a strong correlation, has "memory". You can find a very good summary about it here: **broken link removed**
I would strongly recommend the references, too.
The most widely used pink noise generators are basically white noise sources which are filtered to look like a pink noise in a spectrum analyser, but lack of the unique feature of a real pink noise.
For biological experiments I need a real pink noise which is generated by a self organised process like a plasma discharge or chaotic oscillation (Chua's circuit).

The design problem here is we aren't sure what you need as there are many types of pink noise in nature.
Pink noise filter in electronics is clearly defined by a half octave low pass filter over white noise but the white noise is not clearly defined, as there are both thermionic and pseudo random types that AVERAGED over time give similar spectral density but in SHORT duration are not identical but may sound similar

Although the PRSG has more "structure"because of the dominant octave, the fundamental sequence length frequency. , which can be anything you want but it will be a dominant pattern which can be modulated if you want over decades while adapting the same spectral density by detecting the density of the mid range. octave and normalizing the gain at different fundamental rates.

The PRSG is a long repeating mathematical sequence of steps ( which are the integral of alternating random interval impulses from a short formula similar to a fractal but not recursive like fractals over smaller intervals. This would take several PRSG's in parallel mixed with analog weights.

So you must decide many things to get Pink Noise.

if your source is an impulse of fixed shape or random shape or a filtered step of pseudo random polarity or same polarity or a integrated pseudo-random sequence of alternating polarity and patterns between a range of intervals from n1 to n2

If an impulse what pulse width ( equiv to max frequency ( 100Hz?) or random pulse width
, what range of intervals and what order of filtering.

No filter : ~flat towards frequency of pulse width
Pink Filter ( warm) ~3dB/octave +/-1
Brown Filter (warmer) -6dB/octave

To help us decide what you want, define the purpose? Emulate or Stimulate or compare with a biological response?

If it is simulation, what is the fundamental frequency? 0.001 Hz?

 

[Tony Stewart]

Here is Pseudo Random Sequence Generated (PRSG) sound over the audio spectrum using a Pink Filter, which gives an ideal -3dB per octave above 200 Hz and is higher below this when analyzing a short interval.
Analyzing a longer interval gives the analysis more resolution to see the closer look at the fundamental rate and sub harmonics which extend the bandwidth below the fundamental but give a different shape dependent on the algorithm used.

You can also listen to it but you may not hear the fundamental aberrations which may or may not be important, depending on use.

Top 65k sample spectrum analysis gives narrow spectrum resolution.
Bottom 128 sample spectrum analysis gives broader spectrum resolution and smoother results over a shorter time.

edit
Also note the spectrum range differs by the analysis.
The resolution bandwidth is different for each plot due to the FFT Sample window size so not only are the scales different, the amplitude at 1kHz is different with a different bandwidth.

To play the pink noise, download the file and rename the file to drop the extension .sub and leave .mp3 ( If you have extensions visible.
But if you download and open with Irfanview, it plays directly.

I could also shift the signal downwards in decades so you don't have to build anything. Just play it from a sound card with a DC response. ( e.g. Turtle Beach)

 

[NoiseInstrumentation]

Nobody has any more idea or suggestion?

Dear Sir,
we came across your post while seaching for applications for a 1/f source we have developed and we are currently testing. We work at a University in the field, among others, of the design of instrumentation for low frequency noise measurements. We developed the 1/f source for our own use (to test a new spectrum analyzer we are developing) and we are searching for applications that might justify publication and/or further development of our design. In most cases, for practical reasons, the lower frequency limit for our measurements/characterization is a few tens of milliHz. However, your problem is intriguing and, if you are still interested (I noticed that your last access was a few years ago), we could be interested as well in working on this issue for academic research purposes. We would also appreciate if you could provide a few references (papers, reports, phD thesis) for better understanding the kind of problem you are addressing and the kind of solution you require. I will be happy to provide you with more information once we established a contact. Best regards, Carmine C.

 

[AnalogKid]

This thread is over 4-1/2 years old. Better to start your own thread about your own question, and place a link to this one in your first post for background information.

ak