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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COMMENTS
bernardperu's picture

JhonnyR

 

If Stereophile has the principle of not doing DBT and for you doing so is a matter of principle why oh earth would you even care to read Stereophile? Your statement above suggests you have very extensive knowledge of the content of Stereophile's articles. So you keep reading stereophile's reviews knowing they are irremediably flawed?? How perverse is this?

 

The real question lies on your double blind tested hatred. 

 

Whatever your answer is I will have to assume that your hatred is a broken record and it will just go on.

GeorgeHolland's picture

He probably reads them as I do for the laughs.smiley

JohnnyR's picture

......on your error filled post above so why should I comment on your assumptions? If you wish to worship Fearless Leader then by all means bow down and do so. I myself prefer to ask questions and be skeptical about his "methods" and the reason "why" he doesn't test ALL items under review.

John Atkinson's picture

Andreasmaaan wrote:
It's a pity that some proponents of DBT as the only valid methodology have used the comments thread here to launch personal attacks against JA.

Indeed. I am not sure why I have become a lightning rod for these audio skeptics. Perhaps it is because it is a matter of religious belief on their part - having had extensive experience of blind testing, I rejected it and thus became a heretic in their eyes. Or perhaps it is just our courtesy in allowing them the space on this website to express themselves.

Andreasmaaan wrote:
JA does measure every piece of gear his reviewers review - a practice which ensures that the opinions of the reviewers are grounded in objective data, or otherwise as the case may be.

As my reviewers do not see the measurements until after they have written the review, I take my hat off to them.

Andreasmaaan wrote:
To cut what is risking becoming a lengthy expression of indignation short: thank-you JA for a wise and thought-provoking read.

You're welcome and my thanks to everyone else who appreciated the preprint. It was an honor to have been invited by the Audio Engineering Society to give this lecture - it's not often that you get the opportunity to look back over a 4-decade career!

A Happy New Year to everyone who surfs this site.

John Atkinson

Editor, Stereophile

JohnnyR's picture

You ignore the errors and just plow along blissfully gobbling up the unwarranted praise.

"JA does measure every piece of gear his reviewers review"

As I pointed out above, along with other errors on the part of Andreasmaaan,you do NOT test every piece of gear your reviewers review, but then you pretended that you do in your response. Only certain items are tested by you. Please get your own facts straight if that's even possible for you to do so.

Regadude's picture

Johnny, I wish you a great new year 2013, in which you sell 10 times more of your home made speakers than in 2012. 

Since you sold zero of your speakers in 2012, you need to sell 10 X 0=0 speakers in 2013 to meet this objective. Maybe you can hire George Holland as your director of marketing and sales... 

Get cracking, you have only got 364 days left to sell your quota...

JohnnyR's picture

[flames deleted by John Atkinson]

Unlike yourself Raghead, I will be DESIGNING and BUILDING my own speakers and learning. You do know that word "learning"? Hmmmm maybe you stopped after age 10. You on the other hand will be on here *yawning* and acting the fool and spending your money on Stereophile reviewed crapola.yes

Regadude's picture

So according to you Johnny, everything Stereophile reviews is crapola?! There is not one good piece of equipment that has been reviewed by Stereophile? Hundreds of reviews, not one good product?

But you, in your basement, build quality speakers... 

I have challenged you before (as well as George) to name your gear. What kind of gear merits the Johnny seal of approval? 

As always, you always ignore my challenge (George chickened out to). It seems you can only complain, but cannot even provide a list of your gear. 

I guess ever seeing pictures of your "famous" speakers is also out of the question. 

All talk and no action. 

Regadude's picture

So Johnny, where are your speakers pics and specs?

In your imagination.... [flame deleted by JA]

GeorgeHolland's picture

Johnny never offered to show you anything other than his backside which I think is approriate considering the childish actions of yourself.What does it matter what our audio components are? Anything we mention would be ridiculed by yourself no doubt. Sorry but I'm not playing your silly game. Good God grow up and act like a man for once will you? angry

John Atkinson's picture

JohnnyR wrote:
As I pointed out above . . . you do NOT test every piece of gear your reviewers review, but then you pretended that you do in your response. Only certain items are tested by you. Please get your own facts straight if that's even possible for you to do so.

Out of morbid curiosity, I looked at the past 15 issues of Stereophile - we published 98 full reviews and follow-up reviews. Of those 98 reviews, 83 were accompanied with a full set of measurements, or 84.5%. So even if not every review includes measurements, the vast majority do, which supports Andreasmaaan's point.

I have explained to you before, in other comment threads, why we do not publish measurements of analog playback components, which is due to lack of resources. I have also explained to you why we do not publish measurements of tweaks, which is that it it is difficult to determine exactly what to measure. I don't see any reason to reopen those discussions, but that you continue to be fixated on these two issues and continue to raise them is sad.

And, as I have warned you, JohnnyR, I am continuing to delete comments from you, and others, that are nothing more than flames aimed at other readers.

John Atkinson

Editor, Stereophile

JohnnyR's picture

"Reviews" means just that, any item reviewed by your staff. If you think "tweaks" don't qualify then they should be labled as "Opinions" not a review.angle All of those full reviews you speak of were what speakers, amps, preamps, cd transposrts and the like?

Yeah I know why you don't test tweaks, that would involve you using those horrible SBT or DBT. That's a really nice system you have set up. "We don't believe in DBTs or do them or can't afford to do them"......"We don't know what to test on the tweaks"..........add the two up and you get "We don't have to show that tweaks actually do anything other than what our "reviewer" subjectivly alludes to in their sighted biased listening using their golden ears"......EXCUSES Mr Atkinson plain and simple. no

Once more I ask you to read and comment about this link:

http://forums.audioholics.com/forums/loudspeakers/83412-diy-loudspeakers...

You seem to think DIY can't do anything right in your previous post in answer to Raghead. Insulting intelligent people that actually build better speakers than the status quo can produce is beyond being pompus in your case.THAT is what's SAD.

Don't you have some real work to be doing instead of being on the forums? I thought that was Ariel's job. Let him earn his pay.

ChrisS's picture

JRusskie,

Look up "fixation" and "perseveration" in your dictionary. "Absolute truths" regarding audio products seems to exist only in your basement and in your head.

John Atkinson's picture

JohnnyR wrote:
John Atkinson wrote:
I looked at the past 15 issues of Stereophile - we published 98 full reviews and follow-up reviews. Of those 98 reviews, 83 were accompanied with a full set of measurements, or 84.5%. So even if not every review includes measurements, the vast majority do, which supports Andreasmaaan's point.

"Reviews" means just that, any item reviewed by your staff. If you think "tweaks" don't qualify then they should be labled as "Opinions" not a review.angle

I am not sure what you mean. You were objecting to Andreasmaan's statement that Stereophile accompanies its reviews with measurements as not being true. I offered the analysis above to show that he was correct.

JohnnyR wrote:
Once more I ask you to read and comment about this link:

http://forums.audioholics.com/forums/loudspeakers/83412-diy-loudspeakers...

You need to consult with your fellow traveler GeorgeHolland, who criticized me about linking to other sites :-)

JohnnyR wrote:
You seem to think DIY can't do anything right in your previous post in answer to [Regadude.] Insulting intelligent people that actually build better speakers than the status quo can produce is beyond being pompus in your case.THAT is what's SAD.

With respect, you are arguing with the voices in your head here. I haven't written anything about DIY speaker designers not being able to do "anything right." What I have said is that a DIY designer, like yourself, doesn't subject his loudpeakers to the scrutiny of a disinterested marketplace, something professional designers do as a matter of course. So the question whether or not DIY designs are superior to commercial designs isn't put under independent scrutiny. It remains unsupported conjecture, as far as I am concerned.

John Atkinson

Editor, Stereophile

GeorgeHolland's picture

Mr Atkinson, you could  compare DIY against manufactured speakers but of course you won't. Might upset those that can't make good speakers and I'm not talking about the DIY cheeky

Johnny plainly stated that "tweaks" are reviewed in your magazine and online yet they aren't tested, hence you don't test every component under review. You have a reading comprehension problem? How many components reviewed by Jason Serinus have been tested? uh huh, right.

So now you wuss out about commenting on links? That proves you had nothing to say in the first place about it so you shouldn't have opened your mouth.Cop out time for Mr Atkinson.

The only unsupported conjecture on here are your abilities to print honest reviews. Your ability to avoid testing  alot of audio components is well known by now. Very impressive spinning you do on here.wink

John Atkinson's picture

GeorgeHolland wrote:
Mr Atkinson, you could  compare DIY against manufactured speakers but of course you won't. Might upset those that can't make good speakers and I'm not talking about the DIY cheeky

Back in the early 1990s, Stereophile's Corey Greenberg was one of the judges for a DIY loudpeaker competition in San Francisco. There were 2 winning designs and as part of the prize, those 2 speakers were subject to a full set of measurements in Stereophile, published in the March 1992 issue. The speakers' measured performance was good but not great and certainly didn't embarass professional designers.

GeorgeHolland wrote:
Johnny plainly stated that "tweaks" are reviewed in your magazine and online yet they aren't tested, hence you don't test every component under review. You have a reading comprehension problem?

I don't believe so. JohnnyR was wrong, in that we very rarely publish full reviews of tweak products. Of the 98 reviews published in the magazine January 2012 through March 2013, there was just one review of a "tweak," Robert Deutsch on the HiFi Tuning Supreme Fuses in May 2012. ( I don't count the AudioQuest power strip reviewed by Kal Rubinson's review in December 2012 as Kal didn't make any comment on its sound quality, only on its utllity.)

GeorgeHolland wrote:
How many components reviewed by Jason Serinus have been tested? uh huh, right.

The correct answer is none. But that doesn't support JohnnyR's case either, as Jason's reviews are published on the website Secrets of Home Theater and High Fidelity, which has no connection with Stereophile. I hardly believe I am obliged to support reviews of products in competing publications with measurements in Stereophile.

John Atkinson

Editor, Stereophile

JohnnyR's picture

"Back in the early 1990s, Stereophile's Corey Greenberg was one of the judges for a DIY loudpeaker competition in San Francisco. There were 2 winning designs and as part of the prize, those 2 speakers were subject to a full set of measurements in Stereophile, published in the March 1992 issue. The speakers' measured performance was good but not great and certainly didn't embarass professional designers."

Golly "only" 20 years ago and as we all know, nothing new has happened since then to make speaker design any better (Insert BIG sarcasm face here) cheeky Talk about a lame example Atkinson.

Yeah yeah, "full reviews" whatever, Plenty of "little revews" though all the freakin time and all they are , are OPINIONS but you know what? You let your reviewers get away with murdering the intergrity of the audio world with their stupid banter about  "blacker backgrounds,lifted veils and HUGE improvements in the sound" without them having to justify their claims, Pretty slick there pal.

Oh and Jason Serinus "reviews" as posted about the recent RMAF isn't connected to Stereophile? Give us all a break, Your EXCUSES are even lamer this time than usual.

Yep typical Fearless Leader goobley gook. Did you major in Universisty in the double speak of Orwell's 1984? If not then you are gulity of plagiarizing the concept.

John Atkinson's picture

JohnnyR wrote:
Golly "only" 20 years ago and as we all know, nothing new has happened since then to make speaker design any better...

Again you are arguing with the voices in your head, JohnnyR. Of course a lot has happened in the past 20 years, especially the advent of low-cost measuring equipment. But you're missing my point, which is, as I wrote earlier today, that a DIY designer doesn't subject his loudpeakers to the scrutiny of a disinterested marketplace, something professional designers do as a matter of course. You have repeatedy claimed that your speakers are as good as if not better than commercial designs. However, unlike engineers like Kevin Voecks, Paul Barton, Richard Vandersteen, Jeff Joseph, etc, your ability to pay your mortgage and feed your family doesn't depend on your skill as a speaker designer. Their's does, and it makes a difference.

Look, if you seriously believe your speaker designs are fully competitve with commercial designs, email me your measurements. I'll get back to you with my interpretation of what they mean, assuming they are as comprehensive as what I publish with every Stereophile speaker review. Put up or shut up.

JohnnyR wrote:
Yeah yeah, "full reviews" whatever, Plenty of "little revews" though all the freakin time and all they are , are OPINIONS but you know what? You let your reviewers get away with murdering the intergrity of the audio world with their stupid banter about  "blacker backgrounds,lifted veils and HUGE improvements in the sound" without them having to justify their claim...

You're not making sense. "Andreasmaaan" was discussing reviews in the magazine being accompanied by measurements. I was discussing reviews in the magazine being accompanied by measurements. You seem to be discussing something that exists only in your mind. And unlike Professor Dumbledore's quote, that doesn't mean it's real :-)

JohnnyR wrote:
Oh and Jason Serinus "reviews" as posted about the recent RMAF isn't connected to Stereophile?

That was a show report. No-one other than yourself equates a magazine's coverage of a show with its formal equipment reviews. Are you seriously suggesting that magazines shouldn't publish show reports without including a full set of measurement data for each room they report on? Really? There isn't an audio magazine or website that does that.

John Atkinson

Editor, Stereophile

JohnnyR's picture

Go have another pink drink Fearless Leader.

Me let YOU interpet my frequency response? Don't make me LAUGH. You can't even interpept Wilson't ragged ass frequency response laugh

[usual flames deleted by John Atkinson]

John Atkinson's picture

JohnnyR wrote:
John Atkinson wrote:

Look, if you seriously believe your speaker designs are fully competitve
with commercial designs, email me your measurements. I'll get back to
you with my interpretation of what they mean, assuming they are as
comprehensive as what I publish with every Stereophile speaker review.

Me let YOU interpet my frequency response? Don't make me LAUGH.

You make my point for me, JohnnyR. It was a serious offer on my part. Professional loudspeaker designers send out their products for review and for the public scrutiny of possible customers. Amateur speaker designers, such as yourself, are often afraid to let anyone else judge their work.

John Atkinson

Editor, Stereophilee

Regadude's picture

I have been challenging Johnny tp provide pictures and or the specs of his speakers. He has never met my challenge.

Now the editor of Stereophile offers to look over his data. Johnny again makes up excuses to avoid providing any information on his heavenly speakers.

Big talker...

bernardperu's picture

Dear Jon,

What should have been an enlightening discussion of your great lecture has been contaminated by ill-conceived comments. Some individuals have posted comments that have created an environment of nastiness. 

I would seriously urge you to start deleting ill-conceived comments from now on, whether they use flamable language or not. Some people are just turned on by the flames, but others aren't. And those others would much rather focus on the joy of engaging in the music and exchanges related to it.

You do not run a state-owned site but a private one that is likely to become a lot less lucrative (in all senses) if such nasty comments are to become visible.

I am not even pointing out names and we all know who I am talking about.

I am just giving you feedback that comes from an avid reader of Stereophile online. 

Finally, the correction of my use of English was mentioned by one of these individuals. Please allow me to say that English is my second language and it is oxidized. Sorry about that. 

Thanks!

 

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