The 2011 Richard C. Heyser Memorial Lecture: "Where Did the Negative Frequencies Go?" “What Happened to the Negative Frequencies?” & Science, a Digression

"What Happened to the Negative Frequencies?"
Nothing happened to them, of course, as I will show, but you mustn't forget that they are always there.

Everyone in this room will be familiar with the acronym "FFT." The Fast Fourier Transform is both elegant and ubiquitous. It allows us to move with ease between time-based and frequency-based views of audio events. You will all be familiar with the following example. Here is the waveform of a short section of a piece of music:

And here is the spectrum of that music:

This usefulness of the FFT algorithm—or, more properly, the Discrete Fourier Transform—is everywhere you look in modern audio. If all we had to use were the tubed wave analyzers of my university lab, a life in audio would be very different and very difficult. But I don't like to use tools without understanding how they work—my physics lecturer at university used to yell that we must always try to examine matters from first principles—so in 1981, when got my first PC, a 6502-based BBC Model B, I wrote a BASIC program to perform FFTs, based on an algorithm I found in a textbook. (The computer took around five minutes to perform a 512-point FFT—debugging the program took forever!) This was the process I followed in that program:

1) Capture the discrete-time impulse response of the system

My FFT satori was to realize that you needed to restrict, to window, the impulse response, then stitch its end to its beginning.

Now you have a continuous wave with a fundamental frequency equal to the reciprocal of the length of the windowed impulse, and the FFT algorithm gives the frequency-domain equivalent of that continuous waveform. However, this was the spectrum I obtained from that program:

You get two spectra: one with positive frequencies, corresponding to ei (angular frequency), the other with the same amplitudes of the same frequencies but with a negative sign, corresponding to e–i. You can visualize this as the spectrum being symmetrically "mirrored" on the other side of DC. The negative spectrum is discarded—or, more strictly, you extract the real part of what is a complex solution, and subsequently work with the modulus of the spectrum; ie, the sign is ignored.

But note the assumptions you have made: 1) the fabricated continuous wave extends to ±Infinity, which is untrue—even a Wagner opera has to eventually end—and 2) what happens at the point where the end of the impulse response is stitched to the beginning? What if there is a discontinuity at that point that mandates you having to apply some sort of mathematical "windowing" function to remove the discontinuity from the impulse response data? (Programs using FFTs should have a "Here Lie Monsters" pop-up when you apply the transform before you've checked that you're using the right window for your intended purpose.) And you have made a value judgment only to use the positive frequencies. While having done so will not matter if, for example, you are concerned only with the baseband behavior of a digital system, it will matter under different circumstances—as I will show when I get on to digital systems.

Note also that the frequency resolution of the spectrum is directly related to the length of the time window you used. If that window is 5 milliseconds in length, the datapoints in the transformed spectrum are spaced at 200Hz intervals, which is not a problem in the treble but a real problem in the midrange and bass.

The title of my lecture is therefore a metaphor: You cannot assume that the assumptions you make as an engineer will be appropriate under all circumstances. You almost need to know the result of a calculation before you perform it.

Science: A Digression
I referred earlier to using tubes in my engineering education; pocket calculators were not introduced until after I graduated from university, so my constant companion back then was my slide rule.

My attitude to science was conditioned by my trusty slide rule. Slide rules are elegance personified: not only do you need to have an idea of the order of the answer before you perform the calculation, a slide rule prevents you from getting hung up on irrelevant decimal places in that answer. And you can't forget that, even when you obtain an answer, it is never absolute, but merely a useful approximation.

In physics, you learned to believe one impossible thing before breakfast every day. The strangeness starts when you learn that a coffee cup with a handle and the donut next to it are topologically identical. When you learn that a stream of electrons fired one at a time at a pair of slits in a barrier create the same interference pattern as if they had all arrived simultaneously. And by the time you get to string theory, it's all strange: if you read Leonard Susskind's books, you will find that string theory predicts that every fundamental particle in the universe is represented by a Planck-length tile on the surface of the universe, and that the surface area of the universe just happens to be exactly equal to the sum of the areas of those tiles. Nothing in audio is that strange!

However, when Susskind writes things like "quantum gravity should be exactly described by an appropriate superconformal Lorentz invariant quantum field theory associated with the AdS boundary," my eyes glaze over, and I reach for that donut and coffee I mentioned earlier. But when you study physics, deep down you grasp that "Science" never provides definitive answers, or even proof. Naomi Oreskes and Erik M. Conway wrote in their 2010 book, Merchants of Doubt: "History shows us clearly that science does not provide certainty. It does not provide proof. It only provides the consensus of experts, based on the organized accumulation and scrutiny of evidence."

And that evidence is open-ended. Even with that scrutiny, there are always the outliers, the things that don't fit, that are brushed aside. I am reminded of the old story, which I believe I first heard from Dick Heyser, of the drunk looking for his keys under a street lamp. A passerby joins in the search, and after a fruitless few minutes, asks where the drunk has dropped them. "Over in the bushes," answers the drunk, "but it's too dark to look there."

The philosopher Karl Popper said, "Science may be described as the art of systematic oversimplification." This as true in audio as it is in science: As Richard Heyser explained in 1986, when it comes to correlating what is heard with what is measured, "there are a lot of loose ends!" It is dangerous to be dismissive, therefore, of observations that offend what we would regard as common sense. In Heyser's words, "I no longer regard as fruitcakes people who say they can hear something and I can't measure it—there may be something there!"

Which brings me to the subject of testing and listening

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COMMENTS
JohnnyR's picture

......blind testing mentioned by a person that doesn't believe in doing them. Aren't they "too difficult" according to yourself? Wait......nevermind just don't answer that because I know it will end up with you Mr Atkinson making some EXCUSE as to why you can't do blind tests for the magazine when it comes to reviewing products. ZzzzzzzzzzZzzzzz.

John Atkinson's picture

JohnnyR wrote:
Sure is a lot of blind testing mentioned by a person that doesn't believe in doing them.

A man sees what he wants to see and disregards the rest, eh? In the 15,000 words of this preprint, there are just a few paragraphs devoted to a discussion of blind testing.

JohnnyR wrote:
Aren't they "too difficult" according to yourself?

As I say, I took part in my first blind test 35 years ago and since then have been involved in well over a 100 such tests, as listener, proctor, or organizer. My opinion on their efficacy and how difficult it is to get valid results and not false negatives - ie reporting that no difference could be heard when a small but real audible difference exists - was formed as the result of that experience.

John Atkinson

Editor, Stereophile

GeorgeHolland's picture

In other words JohnnyR, Mr Atkinson DID find excuses not to use blind testing but found them worthwhile enough to mention them in his Heyser speech funnily enough.

JohnnyR's picture

A. Join a band as a second rate bass player

B. Fail to get a record contract

C.Pretend he's an electrical engineer

D.Get an offer to ruin.....ermm I meant run Stereophile

E. Proceed to ruin........ermmmmm excuse me......run Stereophile like Hitler would.

F. Spend his time talking online instead of actually doing any real work.

G. Make excuss about his busy schedule and why he can't do DBTs

H Profit!!!

Regadude's picture

Johnny makes plywood boxes in his mother's basement, and then claims he is a speaker expert.

Trolls audio websites. 

 

That is all.

ChrisS's picture

JRusskie seems to have become a failed audio (and DBT) expert in one easy step...

 

A. Failed...

dalethorn's picture

Hitler? I don't know whether to laugh or cry.

Ariel Bitran's picture

also, brings both of these to mind:

http://en.wikipedia.org/wiki/Reductio_ad_Hitlerum

http://en.wikipedia.org/wiki/Godwin's_law

ChrisS's picture

There it is, again...

ChrisS's picture

I think a synapse just exploded...

dalethorn's picture

I asked a question of Harman Testing Lab in the Computer Audiophile forum, and post #11 is the answer, which I thought was perfect. i.e., let the testee control the switch, so whatever adjustment time they need they can accomodate.

http://www.computeraudiophile.com/f12-headphones-and-speakers/behind-har...

Other observation: The comments in this Stereophile article about the noise floating free of the recording due apparently to having a higher playback bandwith - that made my day.

On R.C. Heyser: His description of the 1971 Sylmar quake, hearing a low-frequency "tone" prior to the shaking, got him started on comparing earthquakes and woofers and low-frequency playback in rooms, and he got beat up on a lot for those writings. But having been involved with both, those observations of his were like gold in the bank. Saved me lots of money.

Regadude's picture

Aren't you the dude who "tested" the Shure SRH 940 headphones and claimed they were almost as good as the 800HDs from Sennheiser?

I own the SRH940s. I was somewhat willing to believe you, but when I saw that your source was an Ipod, I just flicked your review in the trash.

You chose a 200$ source to test 325$ and 1500$ headphones?  And you believe your results mean something?

 

no

dalethorn's picture

My review of the 940, agreed upon by more than 95 percent of respondents, was vetted with specific music tracks listed in the review and subsequent comments, using ipods alone, ipods with analog amps, and desktop DACs and amps. Some of the naysayers are either impatient or just grumpy and disagreeable, which the comments in this Stereophile article perfectly illustrate.

Regadude's picture

How nice of you to call people who question your methodology grumpy, disagreable, etc. I question your methodology because it makes no sense to test 325$ headphones with an ipod. It makes even less sense to test 1500$ headphones with an ipod...

I actually listened to the Shure SRH940 and HD800 today, using my ipod Nano. You are correct, they both sound almost the same. They both sound like shit!

I know from experience that these headphones really shine with a good source, and especially, proper amplification. As good as the Shure is (I own them), it is no match for the HD800 when both are hooked up to decent equipment.

Your test is like testing the acceleration of a Ferrari and a Prius in your 12' driveway. You won't get much better results from the Ferrari in such a limited distance.

As for the 95% who agree with you, what gear did they use (ipod)? Were those 95% SRH940 owners and fanboys? 

dalethorn's picture

Saying "they both sound like shit" when one of those is a revered $1500 headphone of great pedigree and popularity among actual audiophiles is telling of your judgement. I would suggest taking a deep breath, pick a headphone and some music tracks you like, then tune out the matrix and just enjoy your music. You'll be less grumpy that way.

Regadude's picture

Don't try and hide behind my words! They both sound like shit through an ipod! What a weasel you are. I did not say the 800HD sounded like shit... BUT IT SOUNDED LIKE SHIT THROUGH AN IPOD. You rigged your test, Dale. 

Again, you use insults...

 

dalethorn's picture

A long time ago one person on a big audio site challenged people like you to be more specific instead of throwing words like s**t around. There were just two persons who offered test tracks with which to compare those headphones, but everyone else (like you) just threw out expletives, and a couple members even made serious threats. Now I have over 30 years experience comparing headphones like the Stax and Sennheiser series, and quite a bit of time invested with the Audio Engineering Society as well as reading Stereophile magazine, so even if nobody in the world were to agree with my conclusions, I'm certainly qualified to test and evaluate these devices. I'd suggest you refrain from purely ranting with words like s**t and offer specific testable facts, or just go away.

This article may help you:

http://dalethorn.com/Headphone_Ipod_Versus_Amp.txt

dalethorn's picture

BTW, and speaking of Prius and Ferrari, you may be one of the better off who don't mind paying $1500 for a headphone and then shelling out $2000 for a headphone amp. But let's pretend for a moment that you have to pinch pennies to get those luxurious goods, so when you finally have them you really appreciate what you have. In this latter case, were you to stumble across an ipod touch or iphone of recent manufacture, with the new Earpods ($29 purchased variety only) being driven by the Dirac DSP player, and had an opportunity to listen at length, it might make you ill to realize what you got for your $3500.

Regadude's picture

My headphone amp is a whopping 400$ (CI Audio VHP 2).

I do pinch pennies. The VHP 2 and the Shure 940 are mine.The Sennsheiser 800HD I borrowed from a friend.

Stop trying to cloud the issue with non relavant issues.

Regadude's picture

How about we let Stereophile test both headphones! First through an ipod, then with decent equipment!

Both headphones sound similar through an ipod.

Plug them into a receiver, they sound less like shit.

Plug them into a decent headphone amp, and they both sound MUCH BETTER. BUT the Sennsheiser pulls away and wipes the floor with the Shure.

Buy yourself a CI Audio headphone amp (the one I use), or any other decent headphone amp Dale... Before buying a 2500$ DAC to install on an ipod.

DUH...........................

GeorgeHolland's picture

The continuing saga of ChrisS being a troll and all around noncontributing poster. Classy act there ChrisS.

Mostly what I got from Mr Atkinson's article was the amount of photos of himself rather than Mr Heyser. I suppose a memorial lecture should be all about the presenter and how he sees fit to turn it into reasons why Stereophile does what it does regarding testing and the lack there of.

"Yes, what you think you are hearing might by dismissed as being imagination, but as the ghost of Professor Dumbledore says in Harry Potter and the Deathly Hallows, "Of course it's all happening in your head, Harry Potter, but why on earth should that mean that it is not real?"

Oh I see now. Stereophile's philosophy is based upon a ficticious Harry Potter character who spouts that what we hear is real.I'll be sure to let those people being treated for such voices in their heads that all is well and medication is not necessary.

"Footnote 2: For a long time, I've felt that the difference between an "objectivist" and a "subjectivist" is that the latter has had, at one time in his or her life, a mentor who could show them what to listen for. Raymond was just one of the many from whom I learned what to listen for."

Well if only that was true. Your readers tend to all be subjectivsts who aren't trained what to listen to but blindly ( I made a pun there since blind testing is not wanted at Stereophile) believe whatever they think they hear as the truth when in fact measuremnts will show that either they heard nothing related to the measurements or perhaps it's Dumbledore once more in their heads, make believe or wishful hearing.

All in all I found your presentation 90% about yourself and Stereophile and reasons why you defend subjective listening and gloss over things like cables and doing serous testing and throwing in various quotes and ambiguous stories barely related to the subect you were supposed to be talking about, unless that subject was muddling the understanding of Stereophile and telling everyone your own personal history instead of Mr Heyser's.

"Third, one well-known skeptic sitting in the audience tonight criticized my abstract a few weeks back on the grounds that I am just offering "hypotheses about stuff that might be just to stir the pot, while offering no real explanations."

Class act there Mr Atkinson, speak out and criticise someone you don't like or agree with in the audience who then has no opportunity to speak up and address the audience themselves. Very childish and immature.I already see how you do the same on here. "My way or the highway"

JohnnyR is once more sadly correct, Blind testing is not and wil not be used by Stereophile. Just because you Mr Atkinson, know how to push a few buttons to measure speakers, does not make you even close to the same league as Mr Heyser was. He furthered the cause of objectivity and made Audo magazine the best audio magizine there ever was. The Audio Critic is a very close second. Mr Aczel used to be one of the worst subjectivists around untill he admitted to being such and saw the light and spoke out against foolish subjective reviews. Testing will always be the most important part of audio magazines. Simply letting reviewers spout off about "blacker backgrounds" "lifted veils" or other such nonsense belittles both the reader and the so called reviewer not to mention the product under "test". Truth in testing is what Mr Heyser strove for not some silly review about rainbow foil, magic bowls or pebbles.

John Atkinson's picture

George Holland wrote:
Mostly what I got from Mr Atkinson's article was the amount of photos of himself rather than Mr Heyser. I suppose a memorial lecture should be all about the presenter and how he sees fit to turn it into reasons why Stereophile does what it does regarding testing and the lack there of. I found your presentation 90% about yourself and Stereophile...throwing in various quotes and ambiguous stories barely related to the subect you were supposed to be talking about, unless that subject was muddling the understanding of Stereophile and telling everyone your own personal history instead of Mr Heyser's.

You have misunderstood the nature of the lecture, GeorgeHolland. The Richard C. Heyser Memorial Lectures are not intended to be _about_ Dick Heyser but instead are offered to honor his memory. The invitation for me to be the October 2011 lecturer clearly stated that I was free to choose any subject I felt appropriate; my triple career as a musician/audio engineer/audio editor and the conclusions I have formed as a result of my 4 decades' experience in those careers were felt by the AES Technical Council members to be an eminently suitable subject. 

George Holland wrote:
Class act there Mr Atkinson, speak out and criticise someone you don't like or agree with in the audience who then has no opportunity to speak up and address the audience themselves. Very childish and immature.

The skeptic in question had emailed me before the lecture to let me know he would be in the audience and would take an active part in the anticipated Q&A session. I included this mention in the preprint to give him the necessary opening. As it turned out, he didn't attend, but I saw no reason to delete the point he made.

George Holland wrote:
Just because you Mr Atkinson, know how to push a few buttons to measure speakers, does not make you even close to the same league as Mr Heyser was.

I agree. As you can tell from my discussions of Dick Heyser's writing and thoughts in the preprint, I have an enormous amount of respect for what he achieved. I have never claimed to be his equal, nor would I. But again I must emphasize that the AES Heyser lectures are not intended to be _about_ Dick Heyser. That is your misunderstanding, I am afraid.

John Atkinson

Editor, Stereophile

Rolli666's picture

I am not sure as to why a person would even want to respond to these posts. Some problems really are better ignored as to invoke the spirit of go away.  I for one appreciated this lecture for what it is thank you.

John Atkinson's picture

Rolli666 wrote:
I for one appreciated this lecture for what it is thank you.

Appreciate your comment. It is rare that a magazine writer has the opportunity to gather all his thoughts in one place and I owe a debt of thanks to the Audio Engineering Society for inviting me to do so.

John Atkinson

Editor, Stereophile

 

ChrisS's picture

Whoa! There goes another synapse! Now they're both brain dead... I duelled extensively with JRusskie re: blind testing on the Forums and I daresay, he shot himself many times with his own arguments.

Saga? Can't wait for the movie version!

Sorry, Ariel... I'll try not to let it happen again.

Dunadan's picture

...which is a valuable insight, I think, from this article that Mr. Atkinson has generously preprinted. His stories--which, though I am not a longtime reader, I presume also reflect the history of Stereophile--mirror the tensions found in the philosophy of science between "reality" and "perception", and the question of whether our observations are truly disinterested or if our minds shape how and what we see (or hear). And, really, what exactly does a blind test resolve? That the reviewer likes one piece of equipment over another, presumably without factoring in aesthetics or cost? But "liking" one thing better than another is still a subjective judgment, and who's to say YOU would share that judgment? Never mind the problem of translating sounds heard by another into words on the magazine's page and then back again into the sounds heard by the reader when he or she auditions the gear. Or the issue of whether sound quality can be adequately described by a series of measurements, any more than colour can be described strictly in terms of wavelength, or consciousness in terms of vibrating atoms in your brain. That's not to say these things aren't significant, but to say that they add up to the sum of our human experience is absurd.

Thanks for a reflective and enjoyable article (at least in my mind).

GeorgeHolland's picture

The purpose of blind testing is soley to see if you can hear a difference between two units. After all the subjective rants of "oh this lifted several veils of crud from the liquid sound" or "I heard a definite improvement" I find it sad that Sterophile keeps saying that DBT or even SBT are not a valid way to test those claims. Either you can hear a difference or you can't yet those that claim they do shy away from proving that fact with a blind test. Afaid they might be shown to be wrong is my opinion, so Stereophile allows them to go merrily along in their own self delusions while spending way too much money on sham products.

ChrisS's picture

In a properly set up DBT, let's say for two amplifiers, what exactly will the listener be listening for?

 

(And what if the lamb heard a difference, but not the shepherd boy?)

GeorgeHolland's picture

Are you seriously so dense that you can't figure it out for yourself? Perhaps that's why you depend upon Stereophile to tell you what to buy?

http://home.provide.net/~djcarlst/abx.htm

http://www.matrixhifi.com/contenedor_ppec_eng.htm

Read and learn.

ChrisS's picture

So Georgie,

If the lamb can hear that Amp A can make the test system sing in a range of 10hz-60khz, but the shepherd boy can't hear in that range so can't tell the difference between Amp A and Amp B, which amp should the shepherd boy buy?

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