Yet another fast edge pulse generator

[tggzzz]

So, there is actually no pre-ringing, it's just an artifact of interpolation?

Interpolation is irrelevant.

It is the Gibbs phenomenon. That has been known about for longer than electronics have been around!

[KE5FX]

This happens whenever a fast edge is passed through an ideal sinc reconstruction filter in a system with enough time-domain resolution to portray the artifact accurately.  The ripples you see are basically caused by the ripples in the graph of sin(x)/x. 

There are plenty of other low-pass kernels that won't exhibit as much Gibbs ringing -- such as the Gaussian response being discussed farther up the thread -- and ideally the scope would allow you to select from one or two different ones.  But the sin(x)/x kernel has the advantage of being the 'correct' one that will represent the band-limited edge optimally.

If you follow the rabbit hole down far enough, you will meet a fellow named Heisenberg who isn't sure where the exit is.

[texaspyro]

If you follow the rabbit hole down far enough, you will meet a fellow named Heisenberg who isn't sure where the exit is.

He's certainly an evil fellow that kills kittens... 

[rhb]

Physical analog systems are minimum phase.  This has nothing to do with Willard Gibbs and everything to do with Hendrik Bode.

As physical systems are minimum phase as shown by Bode and many others,  using a zero phase sinc(x)/x  is pretty lame in a DSO. as it does not conform to physical reality. and a minimum phase sin(x)/x is no more complex.  It's just a different set of coefficients.

You can make the sin(x)/x interpolator pure causal by applying a Hilbert transform.  While this would be *highly* unusual in seismology (we tend to like symmetric wavelets and routinely zero phase data using impulse responses of the recording system) it does make good sense in electronics.

Gibbs has *nothing* to do with it.  Gibbs did not describe "pre-ringing".  What he showed was that the spike at the peak of a step was a mathematical consequence of the Fourier series. Or to put it differently, if you don't want overshoot you need to modify your step response spectrum.

The more I read  comments about DSP from forum members for whom  I have great respect, the less regard I have for the DSP training of EEs.  I'd always assumed they knew more about DSP than geophysicists,   But then, most EEs do a little DSP, whereas seismic processors do nothing else.  And reflection seismic research scientists spend all their time inventing new DSP algorithms. In general the DSP for reflection seismology is so highly developed that no individual could master all  of it.

FWIW the sin(x)/x interpolator is also called a "Whittaker" interpolator.

Those are the facts and nothing but the facts.  How anyone can involve Heisenberg in this is completely beyond me.  All the mathematics were proved long before I was born.

As a general reference, "Random Data" by Bendat & Piersol 4th ed is the best summary of the subject which was developed  primarily by Wiener, Shannon,  Nyquist and Whittaker in the 30's and 40's.

[KE5FX]

Those are the facts and nothing but the facts.  How anyone can involve Heisenberg in this is completely beyond me.  All the mathematics were proved long before I was born.

There's a very intimate connection between the uncertainty principle and the time/frequency duality encountered in DSP work.  If you haven't encountered that before, it may be a good idea to look into it.  It's pretty neat stuff.

The rest, I'll leave up to others to argue with you about, being (apparently) short on the requisite education and experience.

[rhb]

I don't think that the change in frequency resolution due to windowing has anything to do with Heisenberg.  It's a natural consequence of truncating the time window.  Yes, there is a duality. You can have precise frequency and imprecise time or the reverse.  But I'd love to see how Heisenberg's observation about location and velocity derives from a simple convolution problem.  Is there a convolution hiding in Heisenberg?

The time-frequency resolution issue is why I viewed wavelets with disdain for many years.  However, after reading Mallat's 3rd ed it became clear that the only problem with wavelets was people misrepresenting them.  Mallat addresses my objection to what I often heard at professional society presentations and is in complete agreement with my position on the subject.

Or as I once put it, "if a statement is true in English, it cannot be false just because it is made in another language."

However, that's not my reason for posting.

I've had a pair of Leos pulsers, the square wave and the impulse version, my 33622A and one of Leo's dual channel GPSDOs set to 10 MHz on a 200 MHz DSO.  I can adjust the 33622a in 0.01 Hz steps, 1 ppb at 10 MHz.  It drifts a bit over time but is easily readjusted to be withing 0.5 ppb or less of the GPSDO.  The behavior of the pulsers is quite interesting.  Initially I thought the issue was the size of the TC step, but it turns out that the culprit is air movement.   Wrapping a towel around the pulsers greatly reduced the frequency jitter.

[Berni]

I suppose velocity and position are related in a similar way as frequency and phase are related. But Heisenbergs uncertainty principle also involves Planks length, while we don't really have something like it with frequency. So id say the idea is similar but not the same thing.

Oh and you can see drift in just about anything if you measure it with enough resolution. But measuring frequency and time is the easiest quantity to measure to a really high number of digits. For example i turned a relay into a PIR sensor by simply hooking it up to a high resolution DMM. Putting my hand 50cm above the relay would cause the resistance to start climbing up, removing my hand would make it slowly drop back down. Shining a light from a distance on the relay also had a similar effect (again warming the coil a tiny tiny amount by radiation).

So in theory you could use the pulse generator to detect if the light in your room is on or off provided you measured it carefully enough and had no other outside disturbances.

[rhb]

The Fourier transform is an integration from negative to positive infinity.  As soon as you truncate the integration you are convolving the signal with a sin(f)/f.    That's the source of the time-frequency resolution trade off.  That's 200 year old mathematics.

I had largely ignored wavelets because of assertions that wavelets circumvented that.  After my first reading of "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut, I realized I really needed to read all of Mallat's 3rd ed.  Mallat discusses the implications of Fourier analysis in relation to wavelet analysis in considerable detail.  And the mathematics of wavelets is essential to understanding F&R.

I'm not familiar with Heisenberg's analysis as I never took quantum physics.  But I'd be surprised if a phenomenum described 100 years earlier would get named after someone who reinvented it.  Both form the horns of a dilemma, but very different mathematically.

With a cloth towel wrapped around it, the jitter in the pulser output drops into ppb territory.  There are occasional frequency shifts.  But for periods of up to at least 20-30 seconds  the jitter is almost as good as the 33622A which is specified at under 1 pS and observation shows it is much less than that.  How much less I won't know until I get my LeCroy synced to a GPSDO.  I'm currently looking at the stability of the DSO timebase.

As a consequence of yesterday's experiments I'm going to enclose my impulse unit with glass wool and heatshrink to see how much it improves the frequency stability.  At this moment, the towel wrapped square wave unit which has heatshrink, but no glass wool, is sitting stable within a few ppb of 10 MHz with frequency shifts well below 1 ppb over longer than I want to look at it.  If I get the expected result from adding the glass wool I'll recover the square wave unit.

Modern measurement capabilities are astonishing.  JBeale's inclinometer thread is a great example.  The results he and others got boggles the mind.  A 2 axis version is on my To Do list.  Once it is working I am going to see how accurately I can measure the level of the lake a mile from my house using the elastic deformation of the crust.

[tomato]

There's a very intimate connection between the uncertainty principle and the time/frequency duality encountered in DSP work.  If you haven't encountered that before, it may be a good idea to look into it.  It's pretty neat stuff.

The two ideas are totally unrelated.

[KE5FX]

The two ideas are totally unrelated.

No, they are not.

I'd be curious to understand why so many people seem to take the idea as some kind of personal affront.  It seemed like an uncontroversial thing to post at the time, and it seems like a pointless hill to die on now. 

I don't see why the relationship between Fourier theory and the uncertainty principle should evoke any reaction stronger than the one I had when I first encountered it, which is, "Hmm, that's kind of neat."  What am I missing?

[tomato]

The two ideas are totally unrelated.

No, they are not.

Not sure how this sentence should be interpreted:

1) "No, they are not related."

or

2) "No, they are not totally unrelated."

[Leo Bodnar]

Not sure how this sentence should be interpreted.

Werner says: "Trying to interpret a sentence might affect its meaning."

[KE5FX]

2) "No, they are not totally unrelated."

That would be #2.  They are not unrelated, at least according to that particular essay from the American Mathematical Society, the reference I posted earlier, and any number of other citations that are similarly easy to dig up. 

Reginald is entirely correct in one respect, which is that I'm distinctly unqualified to pick up a piece of chalk and defend the point.   I'll concede and be satisfied with muttering Eppur si muove under my breath if it will keep peace in the family.

[tomato]

2) "No, they are not totally unrelated."

That would be #2.  They are not unrelated, at least according to that particular essay from the American Mathematical Society, the reference I posted earlier, and any number of other citations that are similarly easy to dig up.

Your link is not to an essay by the American Mathematical Society.

Heisenberg's Uncertainty Principle is about the fundamental uncertainty in observables that arises when their associated operators are non-commuting.  It is strictly a quantum phenomenon.   The equations may look similar to those describing a pair of classical conjugate variables (e.g time & frequency), but they are unrelated concepts. 

[KE5FX]

2) "No, they are not totally unrelated."

That would be #2.  They are not unrelated, at least according to that particular essay from the American Mathematical Society, the reference I posted earlier, and any number of other citations that are similarly easy to dig up.

Your link is not to an essay by the American Mathematical Society.

No, it's to an essay from the American Mathematical Society, more specifically published under their masthead.

I'm done here.  It's been weird.

[rhb]

If I'm standing outdoors and getting wet, being rained on is not the same as getting sprayed with a hose.  Even if the water is falling on me vertically.  In the latter case,  walking a few feet will change things.  That's the best I can come up with as an analogy.  I've seen a lot of stupid errors because people were sloppy about such distinctions.  In particular in geodesy where the errors lead to spending many millions of dollars drilling wells in the wrong location. 

My sensitivity about such things is not personal.  It's the sort of thing I was paid to do. When I terminated my contract with a supermajor in 2007 at 55 and left Houston to look after my parents in Arkansas I had just finished  constructing a 600 x 300 x 6 mile model of rock properties and especially pore pressure in the GoM from a half TB of data..  That work was a regional study.  But I was doing a brisk trade on the side doing pore pressure predictions for individual wells for the deepwater business unit where well costs were typically $50-150 million.  One well I worked on was the third $50 million well being drilled on the prospect.  The other two wells had to be abandoned because of excessive pressure.

Macondo was an organizational failure by BP.  They'd reached TD, but drilling operations blew it while plugging the well.  A rig like the Deepwater Horizon rents for $500,000/day.  They were in a hurry to move move to the next well.  I've not bothered to research it even though I own BP stock as a consequence of working for Amoco in the early '80's.  But from what I've read it appears that the total bill for that disaster was $40 billion.  Do that kind of work as long as I did and you too will be *very* particular about details other people ignore.

Back to the thread topic.

I've got my 33622A linked to the GPSDO and the DSO triggering off the 33622A.  My impulse unit is now insulated with some glass wool and heatshrink.  The square wave unit is just heatshrink with some electricians tape to close off the ends.  Both units are running within 1.5 ppm at a room temperature of 80 F.  The actual error varies by about 1 ppm.  I can adjust the 33622A in steps of 10e-6 Hz.  I'd thought it would adjust in steps of 10e-2, so I'm a bit agog at 10e-6 steps.

At the moment the impulse unit is very stable, but the square wave is jumping around, sometimes fast, sometimes slow and sometimes spot on the 33622A (at 0.9 ppm slow).  Or it was when I started typing.

Now both are jumping around, but I have no way to tell if it's the pulsers or the DSO timebase.  So next up is to sync the LeCroy DDA-125 to the other channel of Leo's GPSDO.

In any case very interesting and fun.

[tomato]

2) "No, they are not totally unrelated."

That would be #2.  They are not unrelated, at least according to that particular essay from the American Mathematical Society, the reference I posted earlier, and any number of other citations that are similarly easy to dig up.

Your link is not to an essay by the American Mathematical Society.

No, it's to an essay from the American Mathematical Society, more specifically published under their masthead.

Am I clicking on the wrong link?  Post #479 ("look into it") -- that link takes me to Quora.com.

[KE5FX]

Am I clicking on the wrong link?  Post #479 ("look into it") -- that link takes me to Quora.com.

There were two links. The link in my first reply to rhb went to a page on Quora where someone asked, "How does the uncertainty principle relate to Fourier transforms?"  The top answer is from a physics prof at Berkeley.  It was just the first thing I found when I Googled for a citation, at a point when I didn't expect to have to defend it like a PhD thesis. 

The second link I posted was the one that went to the AMS website, which was the second thing I found when I Googled for a better citation than the evidently-inadequate one on Quora.

[tomato]

Am I clicking on the wrong link?  Post #479 ("look into it") -- that link takes me to Quora.com.

There were two links. The link in my first reply to rhb went to a page on Quora where someone asked, "How does the uncertainty principle relate to Fourier transforms?"  The top answer is from a physics prof at Berkeley.  It was just the first thing I found when I Googled for a citation, at a point when I didn't expect to have to defend it like a PhD thesis. 

The second link I posted was the one that went to the AMS website, which was the second thing I found when I Googled for a better citation than the evidently-inadequate one on Quora.

Okay, thanks.  I see the second link.

[rhb]

I also got the Quora link.

Heisenberg's principle relates the location of a particle to its velocity which is the time derivative of location.

The time derivative of a sine is a cosine, but the cosine is not the Fourier transform of a sine.  Nor is the time derivative of a Gaussian, a Gaussian.

So there's a rather large step from the time-frequency ambiguity of the Fourier transform to invoking that ambiguity in the case of the location-velocity ambiguity of quantum mechanics.

I am fine with saying that the two are analogous.  What I'm not OK with is saying they are equivalent. Unless you can present a mathematical proof.  And for the reason cited above I find that a serious stretch.  I'd be genuinely interested if that can be shown.  I'll look at the AMS link in the morning.

My 3 year foray into sparse L1 pursuits, aka compressive sensing, took me into Grunbaum's monograph on regular polytopes in N dimensional space.  Which is a *very* long way from literature and philosophy or any applied math I've dealt with previously.  So I'm no longer the least bit bothered by texts written for mathematicians.

Show me.

[tomato]

Heisenberg's principle relates the location of a particle to its velocity which is the time derivative of location.

No.  Position and momentum are conjugate variables, with the momentum operator involving a derivative with respect to position, not time.  (Energy and time are conjugate variables, with the energy operator involving a derivative with respect to time.)

[Leo Bodnar]

There are few problems with quantum mechanics: nobody understands it while popular media dissolved it into memes and jokes which is great but makes everyone (and me too) think they do.
This discussion is fascinating because each side has a valid point.

I am curious whether apparent similarity would be more difficult (or impossible) to defend if the original author turned to matrix representation of quantum mechanics (which is fundamentally identical to wave one.) Heisenberg himself used matrix representation and totally hated and derided Schroedinger's wave form.  Popular media somehow ignores matrix representation (and bra-ket notation at that) - possibly because it's not hipster enough?

By the way, Heisenberg discovered and formulated the uncertainty principle based on matrix representation.

[rhb]

I'm attaching a few pages from "introduction to Quantum Mechanics" b Richard L. Liboff.  I make no claim to understanding quantum mechanics beyond being aware of some of salient characteristics and why it was developed.  Most of what follows is from a 10-15 minute skim of the opening chapters of Liboff.

Matrix notation is just a convenient shorthand, nothing more.  In quantum mechanics one deals with a scalar and a vector in 3 space.

Liboff refers to position and momentum as "complementary variables"  rather than tomato's "conjugate variables".  There are a great many figures which superficially resemble Fourier transform pairs.  They are not unless they deal with the wave nature of particles or instances of the Bohr correspondence principle  which states that quantum mechanics must reduce to classical Newtonian physics in the limit as the quantum number approaches infinity.

There are as many meanings to a sentence as there are readers thereof.  Each of us brings our own set of contextual references which we use to interpret the words.  The "I'll look it up on the internet if I need to know" meme implies that those who endorse that have extremely limited communication skills, even when they are only reading.  It gets far worse when they write.

Back to the original thread topic.

Leo, will the pulsers stand a short across the output?  It seems to me that as they are capacitively coupled they will, but I'd rather ask than ruin one.

[Leo Bodnar]

Leo, will the pulsers stand a short across the output?  It seems to me that as they are capacitively coupled they will, but I'd rather ask than ruin one.

Yes, they are fine with shorted output.
Leo

[rhb]

I've ordered a BNC SOL cal kit from SDR-Kits.  The first iteration of the TDR VNA software will use the impulse unit as it doesn't need as long a delay line, but I plan to make it work with the  square wave unit as well.  I you can only afford one, I think the square wave unit is more generally useful. 

That's certainly true if you work on analog scopes, but may not be as important with current DSO designs as they really don't have much that can be adjusted.  Two trimmer caps in the Instek GDS-2000E line.  I've not been inside the Owon XDS2102A yet, but in 12 bit mode it should provide ~ 100 dB of dynamic range from a single 20 Mpt trace.  That's on par with an 8753 and a pulser and cal kit totals 6% the price I paid for my 8753B w/ 85047A S parameter set.  Obviously not the range of the 8753B, but if you're new to radio, HF is quite hard enough.