The 2011 Richard C. Heyser Memorial Lecture: "Where Did the Negative Frequencies Go?" Case Study 3: Digital Recording & Playback

Case Study 3: Digital Recording & Playback
The title of this lecture asks "Where did the negative frequencies go?" Once we enter the world of digital audio, they are very much present. Here is the spectrum of the music waveform I showed earlier:

And this is the spectrum of the same signal after it has been sampled in the time domain:

The positive (red) and negative (blue) spectra are mirrored around the sampling frequency and all of its harmonics, the latter extending to, if not infinity, then to something practically close to it. If you wish to play back time-sampled data, you need some way of eliminating all those spectral images other than the one in the baseband. Yes, a low-pass filter is required, but that filter turns out to have a very special function: it doesn't just remove the ultrasonic images, it reconstructs the original analog signal (below the Nyquist Frequency, that is, half the sample rate). The pulses representing the sampled amplitude are convolved with the impulse response of the filter to give the original signal, something that I found elegant in the extreme when I first understood it. That convolving is shown here in a diagram taken from John Watkinson's 1986 book on digital audio:

I still marvel at the elegance of this concept. But what if you don't use a reconstruction filter? The effect in the audioband is inconsequential—just a small rolloff in the top octave, due to the aperture effect (the pulses have a finite length).


NOS DAC with no reconstruction filter, frequency response at 44.1kHz sample rate

Above the audioband, the conventional reconstruction filter gives a well-behaved analog signal. Reproducing data representing an equal mix of 19 and 20kHz tones, you get a spectrum in which the inverted images of those tones—the negative frequencies—are well suppressed.


DAC with conventional reconstruction filter, spectrum of 19+20kHz tones with a peak level of 0dBFS

But, my goodness, when we repeat this measurement with a so-called NOS DAC (for Non-OverSampling), which has dispensed with the reconstruction filter, we get this:


NOS DAC with no reconstruction filter, spectrum of 19+20kHz tones with a peak level of 0dBFS

Ugh! There are the negative frequencies in all their glory, as well as a host of related aliasing and intermodulation products dumped back into the audioband.

So why do listeners like this mess? It can't be the aperture effect: –3dB at 20kHz is a subtle change at best. Some propose that it is the improved time-domain behavior of the system that the listeners are responding to . . .


NOS DAC with no reconstruction filter, impulse response

. . . compared with the impulse response of a conventional time-symmetrical FIR reconstruction filter:


DAC with conventional reconstruction filter, impulse response

Yet the differences between these two impulses all fall within the ear/brain's integration period. So unless people like the sound of their amplifiers misbehaving with the ultrasonic image energy, I have no idea what is going on here, other than to say that, whatever it is, it is not elegant.

An idea I did find elegant was Peter Craven's introduction of so-called "apodizing" reconstruction filters. Compare the conventional filter's impulse response above with the impulse response of a Craven apodizing filter:


DAC with minimum-phase, apodizing reconstruction filter, impulse response

The acausal ringing of the conventional filter of both the A/D and D/A converters has been replaced by a larger degree of causal ringing—it occurs after the event instead of before and after—at a slightly lower frequency. (The apodizing filter has a null at the original data's Nyquist Frequency.)

Again, people report that they prefer the sound of apodizing filters. A few years ago I published an article by Keith Howard in which he investigated the behavior of the reconstruction filter. As part of the preparation for that article, Keith sent me DVD-As of music treated with different filters. The recordings weren't identified, but Keith asked some of the magazine's writers to listen to the examples and rank them on sound quality. This was extraordinarily hard to do, but one difference did emerge as being consistently audible under blind conditions. When we were sent the key as to what filters had been used for each example, music reconstructed with the minimum-phase filter above sounded superior to music reconstructed with this filter:


DAC with acausal reconstruction filter, impulse response

Okay—the latter is nothing like we hear in nature. However, why does replacing acausal ringing at a frequency that people can't hear with causal ringing at a slightly lower frequency that people still can't hear result in better sound—er, sound that people tend to like more? Again, as Dick Heyser said, "there are a lot of loose ends!" (footnote 7)



Footnote 7: In subsequent conversations, I have been told that the ear/brain also acts as a wavefront arrival detector, that an acausal filter causes mental confusion as both the initial onset of the ringing and the arrival of the maximum energy peak are incorrectly interpreted as two separate events rather than one.
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GeorgeHolland's picture
No you may address me as

No you may address me as George or Mr Holland. Georie is an attempt at making fun but then again that's about all you know to do anyway.

Please ask a relevant question or just shut it.

The lamb would first have to prove they can hear a difference with a dbt

The shepard can buy whatever he wants.

The big bad wolf tried to convince both that the expensive boutique amp was the one to buy

They told him to shove it and bought a less expensive but well built amp and they all lived happily ever after except for Mr Big Bad who soon folded his shop due to no sales.

ChrisS's picture
Mr Big Bad?

So Georgie,

Let's make this question relevant....

Let's say we're testing two amplifiers with two listeners. The first listener is an 18 year old young lady who is trained in classical piano at a Grade 10 music conservatory level. She can hear that Amp A has an excellent range 16hz-40khz through the test system, but even though Amp B doesn't have the same range, she likes the "sound" of it better.  The second listener is the shepherd boy who's grown up now. He's 54 years old, likes big band jazz, but his hearing has been damaged by working with heavy machinery without hearing protection. He can't hear a difference between the two amps.

 

Which amplifier should the ex-shepherd buy?

GeorgeHolland's picture
The 18 year old can hear to

The 18 year old can hear to 40KHz?  Were her parents bats?

"Like" doesn't have anything to do with blind testing. You don't pick which one you "like" you see if you can tell WHICH amp is playing. You don't even know how a dbt test is run I can see already.

 Who cares which amp they buy?  Maybe the people selling them do but that is completly irrevelant to dbt. You have no clue as to what blind testing is all about.

ChrisS's picture
Real World?

Georgie,

Are you a real person or a computer generated figment from JRusskie's russian clone of an old IBM PC? Do you know anyone with normal hearing? Do you know how real people shop or do you isolate yourself in the sanctuary of your closed mind and order everything on-line after reading extensive reviews in Consumer Reports?

ChrisS's picture
Really?

You call those proper Double Blind studies?

GeorgeHolland's picture
Oh so you are an expert on

Oh so you are an expert on double or single blind studies. The ABX system is a proven dbt way to do things. Just because the results have you so upset, you claim the people doing the testing are doing it wrong? Laughable. Tell me some more jokes.

ChrisS's picture
"Hey There, Georgie (Boy)...

...Swinging down the street so fancy-free..."

 

In fact, Georgie, my major(s) for my undergraduate degree were in Developmental Psychology (including Perception) and Statistics (including Research Methodology). So yes, the set up and methodology shown in those links are crap and the results are laughable...

ChrisS's picture
Run Run, Georgie Boy!

Get thee to a local college and enroll in a first year research methodology course. Have fun learning!

GeorgeHolland's picture
Either address me as George

Either address me as George or STFU you stupid little boy. I think you majored in being a twit and smart ass. Who can take anything you say as serious? Grow the fuck up already. You act out like a lil boy with the IQ of a rock.

Go tell the people who make the ABX test system what you just said and see how they laugh you out of the room. You bring nothing to this discussion other than what you don't agree with , with zero facts to back up your claims. Come on show us all how the ABX test methods aren't any good or why the blind testing done in the othe link was faulty. Better yet tell Harman Kardon that their blind testing techniques are faulty and not worth doing.

ChrisS's picture
Go Ask Alice

Georgie,

You must be running out of neurons if you don't trust your own eyes and ears. Yes, the facts are out there.

JohnnyR's picture
Trusting Ears............

.is what SBT and DBT are all about. Using your eyes to test audio products? Well yes I can SEE that YOU would have to look so you would know which one is "better".

ChrisS's picture
Your ears?

Whose ears? Why?

John Atkinson's picture
Not what I have written

GeorgeHolland wrote:
I find it sad that Stereophile keeps saying that DBT or even SBT are not a valid way to test those claims.

Please do not put words in my mouth. That is not what I have said. What I _have_ written is that to design a blind test that limits the variables to just that which you are interrsted in and that produces valid results when there is a small but real audible difference is complicated and time-consuming. The literature is full of poorly designed and performed blind tests that have been proclaimed by audio skeptics as "proving" that there are no audible differences. Such people demonstrate both their ignorance of the Scientfiic Method and their unquesitoning faith in "Scientism."

John Atkinson

Editor, Stereophile

GeorgeHolland's picture
JohnnyR was right more

JohnnyR was right more EXCUSES.

It's pretty simple Mr Atkinson but then having the will or gumption to put a dbt into the line of testing is the first thing you have to have,

You obviously don't have that or just don't care so it's a moot point anyways.

JohnnyR's picture
George, He Never Has Cared.......

.nor ever will when money is involved.

dalethorn's picture
General observation

I would hate to see magazines and websites like Stereophile become intimidated by naysayers who demand "proof" of everything they say, in advance or after the fact. There's a lot of that in mainstream media, due no doubt to controversial topics and false information being fed to reporters. But come on, people - this isn't a mainstream news outfit reporting life or death stories. We have here an incredibly rich article full of facts that can be researched and questioned with references that are well established over time. Instead we have people questioning the author's motives or his pursuit of truth? I think people who are looking for "The truth" should be looking in a religious forum, not a hi-fi forum. There's very little you can "prove" on these topics - the value here is the very informed opinion that costs you nothing.

Ariel Bitran's picture
Hear Ye

nice comment Dale. as an attendee of this lecture, i can tell you it was surely enlightening.

GeorgeHolland's picture
I think you have it all

I think you have it all backwards there friend.....

"I think people who are looking for "The truth" should be looking in a religious forum, not a hi-fi forum. There's very little you can "prove" on these topics - the value here is the very informed opinion that costs you nothing."

Religion is based upon belief and subjectivists cling to their belief, they don't go looking for proof or the scientific method. No you can't prove very much when the reviewers use subjective say so instead of actually measuring the units. Opinons are a dime a dozen or even less than that and worth next to nothing. Just look at all the opinions here.

dalethorn's picture
No George

No, George, you don't get it. You're still stuck in religion, looking for proof of something. Here you get 'information' only, and if you want 'proof' of something, you have to do the work in proving it to yourself. What *you* believe, outside of yourself, is purely opinion. Perhaps all these people looking for truth or proof are just lazy, and trying to intimidate others into doing the work for them. Like bullies.

JohnnyR's picture
Way To Spin........

......the facts there pal. Your "arguement" is FLAT.  The only "info" Stereophile shows us is what the WANT to show us. Cables, power cords, magic bowls are off the list of even testing them in anyway what-so-ever. The reason? Ohhhhh we really don't know how to test those duhhhhh. How lame an EXCUSE is that?  Stereophile is SUPPOSED to be a magazine for information NOT excuses.

"Perhaps all these people looking for truth or proof are just lazy, and trying to intimidate others into doing the work for them. Like bullies."

 BWAHAHAHAHAH!!! that has to be on my "Top 10 WTF Things of 2012"

 You DIDN'T just say that did you???? So let me get this straight, Stereophiles job as you see it is to just fling out "say so" and it's up to the readers to wade through the muck and mire of those reviews to try and grasp one little bit of truth? Yeah right, you must really love it then because they rarely show any truth at all.

Ariel Bitran's picture
Why

why is it so hard to accept that double-blind listening tests are difficult to achieve as JA has explained in his lecture?

the fact that our existences are commandeered by individual perception based on thousands of variables makes it very easy for me to understand, just as how one person may enjoy spicy foods but not grapefruit or where some may hear too much bass and others not enough. so many VARIABLES!!! culture, upbringing, what sounds you are surrounded by, traffic signals, your genetic structure, your actual physical position when listening. perception is a learned skill that we do not choose to accept, it just happens and it is different for every single person.

i think THESE are the sort of differences between individuals that make DBT difficult: everyone hears differently. there is no absolute sound.

the best example of how an ear and sonic preference can change is in the study of language and sounds. the chinese language has a completely different set of sounds to that of the english language, thus their speaking intonation, laughter, and music reflect their cultural and sonic inclinations. eastern and western and andean and greek and celtic and ... and ... all use completely different scales based on their preferences of sound learned over time through language and their environments.

Thus, i often wonder do hi-fi listeners across the globe prefer different sounding systems based on their installed sonic memory? or is there a constant in terms of preference across the globe? probably not. or even more interestingly, can one find similarities in preferences in sound based on linguistic sounds of an individual region? are the frequencies accented in the german language more easily noticed by a german in his hi-fi? DBTs are a waste of time. instead of focusing why not, it is much more fun to focus on the why.

the heart of all of this lies within JA's question: where do the negative frequencies go? there are aspects to our perception of sound that simply cannot be measured because they are based on individual perception which is different for every single one of us.

GeorgeHolland's picture
If blind testing is so

If blind testing is so difficult then how did the people that I linked to manage to do so?  Harman Kardon does blind testing at the drop of a hat. Go ask them how they do it so easily. Mr Atkinson's refusal to do so is simply an excuse as to not have to bring up why cables, power cords and other snake oil is indeed snake oil. He can merrily go along his way as he has for years now ignoring such products and letting his reviewers say whatever BS they want about the sham products and not have to worry one bit. He just doesn't care is the bottom line.

ChrisS's picture
Puddin' and Pie

Georgie Porgie,

That you cite these links as authoritative sources indicates the level of your understanding of testing methodology.

JohnnyR's picture
ChrisSy You Cite..........

......nothing to back up whatever it is you are trying to say but it is amusing.

ChrisS's picture
Some book learnin'

Research methodology courses are taught in colleges and universities all over the world, even Russia...

Let us know when you and Georgie take one.

JohnnyR's picture
Still Nothing ChrisSy??????

Nothing to cite other than your own wandering silly posts? Thought so.

Regadude's picture
At least Chris...

Well little Johnny, at least Chris is A REAL psychologist. He's not a, you know, a hobbyist like yourself...

JohnnyR's picture
I Haven't Seen Any.........

........credentials from ChrisSy just say so. Oh lets see I think I'll be a nuclear scientist now just because I say I am on the forums. There now it's a done deal. Besides how he acts out is more like a 3 year old than an adult. Some professional he is and tell us all again just what your expertise is? Trolling perhaps?

Regadude's picture
I haven't seen any...

...credentials from Johnny the hobbyist speaker designer. Let's see some pictures of your Johnny brand speakers! Post some pics, or provide a link to a site where we can see these speakers of yours.

I demand to see these speakers of yours! 

ChrisS's picture
If A = B and C = B...

If JRusskie has a misguided and limited understanding of DBT, and....

Georgie has a misguided and limited understanding of DBT, then....

Are JRusskie and Georgie one and the same person?

Has anyone seen them in the same room together? Hmmmm.

Please, one of you (I guess it doesn't matter which...) ask Harman Kardon how they do their DBT's and how they use the results.

Thank you.

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