Audibility of Small Distortions

amirm · Dec 23, 2012

I bet you think there is no connection between room/speaker resonances and other types of distortions like jitter. But there is!

Read this article I wrote for the Widescreen Review Magazine which talks about how the two share common characteristics in their audibility although not remotely in any obvious manner: Audibility of Small Distortions http://www.madronadigital.com/Library/AudibilityofSmallDistortions.html

The article drills into a methodical way we can determine the level of inaudibility based on mathematical analysis and relating that to our hearing threshold.

As usual, comments, suggestions and criticism is all welcome

.

amirm · Dec 23, 2012

Thanks Tom. On the suggestion for the test, you are confusing me with someone much less lazy.

I did make an exception for the next article though. It is the most data intensive one I have done for WSR where I example the role of computing power to optimize room acoustics. It will be out in January/handed out at CES. I will put it online while it has been on news stands for a bit.

microstrip · Dec 23, 2012

Very good Amir.

I really appreciated to read someone fearless writing the words " psychoacoustic principal " and referring that " Sadly I have yet to see anyone do research into what particular music selections are more revealing than others for finding such distortions."

After reading your full post I fear that your next paper be targeted to privileged people - every time you refer to simulations you address solutions that ask a lot of computing power and very expensive and peculiar expertise!

jkeny · Dec 23, 2012

Well done, Amir, glad to see this analysis.
The idea of mutitone testing is also very good & more interesting to evaluate the resulting side spurs.
But is it not true that the the single spur that you show is a very simplified version of actual jitter in a system even with a simple sinewave tone?
Is it not more usual to see many side spurs? Would these not therefore have a more adverse sonic effect as they are further from the fundamental tone & therefore less likely to be masked?
Also of interest is the spreading at the base of the central carrier frequency - this represents close-in phase noise. The current thinking in "jitter circles"

is that this type of jitter is actually the most detrimental to tone. Any thoughts?

amirm · Dec 23, 2012

Yes, we don't really have an easy way to model the typical jitter that actually occurs in real products.

On your question, can you expand? The carrier is music and is made out of all the tones in it so I am unclear by your reference there.

jkeny · Dec 23, 2012

Yes, I suspect that the devil is in the details when real jitter spectra are under consideration & statistical analysis probably becomes very important but equally very dense to understand?

What I mean by carrier frequency is actually in relation to the phase noise associated with clocks where close-in phase noise is the most difficult to remove as it is based on the crystal cut. It is also the most difficult to measure & finally is thought be more sonically detrimental than would have been thought initially. I wondered, based on your graphs if it actually has the same multiple frequency consequences as your low Q example? Even though at a relatively lower amplitude, it may have a proportional higher detriment?

jkeny · Dec 24, 2012

Let me explain what I mean further & correct my thinking if this is wrong
Phase noise for clocks is graphed as follows

This is taken from a Ham radio site where phase noise & close in phase noise is important to be able to effectively tune in to a channel close in frequency to another channel & have no interference between them - no bleeding of one channels signal into another.
Now this makes sense to me as close in phase noise to me means that the clock or oscillator is fluctuating very slightly either side of it's fundamental tone. The level of the line in the graph is a statistical measure of how often it will fluctuate within 0.1Hz, 1 Hz, 10Hz, etc, of it's fundamental tone.
With all clocks this type of plot is seen where the graph rises as the plot gets closer to the x origin i.e the fundamental tone. The next graph expands the phase noise to a more normally seen jitter graph in that the phase noise is mirrored to the other side of the fundamental tone also.

Now here's where it may get fuzzy for me - like in your diagram of Q where low Q has a more sonically detrimentally effect because it's effect spreads over many frequencies, close-in phase noise also has the same spread but over all frequencies because it is a timing error on every clock tick. Whereas the further out spurs in phase noise as are seen in the first graph(s) are somewhat less frequently occurring or effect less frequencies (this is where I'm fuzzy). As I said this is more difficult for me to get my head around because it's a derivative function i.e the clock frequencies are what the music is derived from & not the music signal itself.

Edit: Ok I found an explanation form the site that the above graph comes from

The sampling process is basically a multiplication of the sampling clock and the analog input signal. This is multiplication in the time domain, which is equivalent to convolution in the frequency domain. Therefore, the spectrum of the sampling clock oscillator is convolved with the input and shows up on the FFT output of a pure sinewave input signal (see Figure 2). The “close-in” phase noise will “smear” the fundamental signal into a number of frequency bins, thereby reducing the overall spectral resolution. The “broadband” phase noise will cause a degradation in the overall SNR

jkeny · Dec 24, 2012

I often see people referring to jitter as analogous to wow & flutter from the analogue domain. I have always been uneasy about this analogy but can't say why exactly. Initially it was because I associated wow with low freq modulation at a certain frequency & flutter the same at a higher frequency whereas jitter is much more a broadband effect & comes in different forms, signal correlated & non-signal correlated. But maybe I don't understand wow & flutter well enough? For instance the threshold between wow & flutter is 4Hz (<4HZ=wow; >4Hz=flutter) - I don't know why 4Hz was chosen & I don't know why it is said that fluctuations at 4Hz is sonically the most noticeable.

Edit: Ah isn't WBF great - that's why I come here - it has the answer already posted (by Amir) here http://www.whatsbestforum.com/showthread.php?5378-A-Solution-to-Wow-Flutter

As you see in chart (c) for FM modulation, there is a sensitivity peak at 4 Hz which is hypothesized as being the case due to human evolution of trying to understand speech which itself is a manifestation of temporal masking (see the slide I post earlier). This nicely agrees with the industry recommendation of paying more attention to 4Hz as the most critical frequency for wow and flutter.

Edit: I see that Amir has gone on to discuss my question in that post & I seem to come to a different conclusion to what he does i.e I concluded that close-in phase noise in the clock is more sonically detrimental because it affects more frequencies but I was unsure of my thinking here. On reading Amir's linked post above (which I will need to read a number of times to fully digest it, hopefully), it may be more to do with the ears sensitivity to Frequency Modulation (FM) at low frequencies i.e 4Hz being the most sensitive frequency.

Interestingly, when my DACs or USB transports are evaluated, the first thing that people notice is the bass - everyone says that it is more tuneful & textured, some feel that it has less weight than they are used to but I reckon this has something to do with our accommodation to over-emphasised, one-note bass in a lot of usual playback systems

jkeny · Dec 24, 2012

Amir, you ended that linked post with the words ". (There are other considerations here that I am not covering here just yet.)" Is this thread the "other considerations" or is there more?

Just combining some of what you said on the other thread with what you said in the article here - 20pS jitter is audible & jitter can cause tones to arise beyond the Nyquist. I would like to know of any studies you have come across that deal with how DACs behave when handling these >22KHz tones! I'm particularly interested in the differences in handling them between SD DACs & NOS MB DACs.

I can give you experimental measured evidence for these tones & their folding back into the audio band, if you are interested?

DonH50 · Dec 24, 2012

Note phase noise gets applied to every sample so the output of a DAC or ADC has a little noise around every spectral line, and all multiples of clock and signal aliased or not. Thus, in a sampled system, you end raising the effective noise floor (reducing SNR) as well as adding "skirts" to each signal's center frequency. Phase noise contribution is a little tricky to calculate as the order (and thus slope) changes as you get closer to the carrier; flat far away, then moving to 1/f, 1/f^2, etc. We ned to know the corner frequencies. I have spreadsheets that simplify it a little (phase noise is always a concern for high-speed clocks, whether radar, telcomm, or PCIe/SAS).

I wonder how audible 20 ps random jitter actually is in a musical signal. Now that I can create (small) WAV files I would like to create a few test cases similar to those I did for the clipping thread.

jkeny · Dec 24, 2012

Thanks Don,
I doubt you will hear 20ps of random jitter i.e noise. The oft quoted figure of 100ns or is it 200ns threshold for jitter audibility I always thought applied to pure random jitter?
What might be more interesting would be what amount of close-in phase noise at what frequencies are audible? As I said, I have heard this being cited as the most noticeable & probably most detrimental to sound. But this is probably a difficult one to simulate?

amirm · Dec 24, 2012

jkeny said:
I often see people referring to jitter as analogous to wow & flutter from the analogue domain. I have always been uneasy about this analogy but can't say why exactly....
Edit: I see that Amir has gone on to discuss my question in that post & I seem to come to a different conclusion to what he does i.e I concluded that close-in phase noise in the clock is more sonically detrimental because it affects more frequencies but I was unsure of my thinking here. On reading Amir's linked post above (which I will need to read a number of times to fully digest it, hopefully), it may be more to do with the ears sensitivity to Frequency Modulation (FM) at low frequencies i.e 4Hz being the most sensitive frequency.

I can quickly paraphrase. Masking says that wow flutter at low frequencies such as a few Hertz, has to be inaudible per my article posted here. It simply is too close to the original tone to be audible. Yet, it is clearly audible. The reason it is audible is because its amount is very high -- orders of magnitude higher than jitter in digital systems. At those levels, it starts to change the volume/envelop of the signal. The ear is able to detect volume changes if they are at certain rates. Too slow and it adapts to them and can't hear the change. Too high and it can't hear them. 4 Hz is the peak detection.

For these reasons, there is little we can learn from application of wow and flutter to digital systems. The notion that large amounts of them can be inaudible in analog systems does not at all instruct us to think that large amounts of jitter in digital systems will act the same way. Both frequency and levels are different for the two universes.

Interestingly, when my DACs or USB transports are evaluated, the first thing that people notice is the bass - everyone says that it is more tuneful & textured, some feel that it has less weight than they are used to but I reckon this has something to do with our accommodation to over-emphasised, one-note bass in a lot of usual playback systems

It is an oddity that bass improves or appears to improve that way. In audio compression, when one gets rid of pre-echo, bass performance improves even though one thinks of that as a function of high frequency transients.

amirm · Dec 24, 2012

jkeny said:
Amir, you ended that linked post with the words ". (There are other considerations here that I am not covering here just yet.)" Is this thread the "other considerations" or is there more?

That post is a copy of one I made on another forum a year back. I read through it quickly but couldn't remember what I meant by that! "It is hell getting old."

Just combining some of what you said on the other thread with what you said in the article here - 20pS jitter is audible & jitter can cause tones to arise beyond the Nyquist. I would like to know of any studies you have come across that deal with how DACs behave when handling these >22KHz tones! I'm particularly interested in the differences in handling them between SD DACs & NOS MB DACs.

I actually created test tones that demonstrate that here! http://www.whatsbestforum.com/showthread.php?3808-The-sound-of-Jitter. I simulated it down to the level that my program would go which was around 2 nanoseconds.

jkeny · Dec 30, 2012

amirm said:
That post is a copy of one I made on another forum a year back. I read through it quickly but couldn't remember what I meant by that! "It is hell getting old."

Ah, going upstairs & then trying to remember what you went up for is worse!

I actually created test tones that demonstrate that here! http://www.whatsbestforum.com/showthread.php?3808-The-sound-of-Jitter. I simulated it down to the level that my program would go which was around 2 nanoseconds.

Thanks, Amir!

jkeny · Dec 30, 2012

Just to correlate with your jitter test tones, here a paper which makes this statement

This entire discussion focused on sampled data systems, but
nowhere were the effects of aliasing mentioned. All of the
equations derived above assume there is no aliasing. The bandwidth
of the jitter is considered to fall entirely (and conveniently)
into a single Nyquist zone. If the jitter is bad enough, and the
signal close enough to a Nyquist edge, the noise caused by jitter
can alias back in band, degrading SNR even further

Little known characteristics of phase noise http://rfdesign.com/mag/littleknown.pdf

DonH50 · Dec 31, 2012

Note aliasing in this context applies to ADCs, not DACs...

jkeny · Dec 31, 2012

Anybody who has a login account at DiyHiFi.org can see the many interesting graphs posted over on this thread from a while back entitled "Some jitter analysis - and beating of a dead horse.." These graphs were taken on SPDIF while playing music & not just single tones using a Lecroy Wavelength scope.

This is one of the posts taken from that thread:

Again, I do think I had seen some simple things confirmed: I can repeat the Hawksford test, and see the same thing again. For me it also shows the "validity" of my test setup.
Also, consider that those simulations/ measurements were done at 1nsec jitter level, in his article!
I'm repeating it at a much lower level, and the phenomenon still valid and functional, with a real device, much better performing than the original setup was.

For me the "jitter foldback" effect was unknown up to know.
But, it would reinforce a good bit of my real life experience: that jitter is easily mucking up also the low frequency range, not only at the upper end.
This small stupid "violins" test suggests that a hard, "brrigth" effect can be produced at midband, while playing a range of only high frequencies. That is quite like the "digititis" what I know oh so well..

Then, about the missing modulation with music: I think it is a moving target. How is the dynamics are evolving in the music? Arches are always relatively low dense spray of high frequency excitation - and the response can be ~ relatively high jitter products in the low-midband!
Also, what if we were looking only at those "slices" of the audio signal, which are in the vicinity of zero crossing. I could imagine, that in that restricted sample range the temporary jitter spectra could show higher jitter levels even with real music..

http://www.diyhifi.org/forums/viewtopic.php?p=44824&sid=4976db3fc4d67f61f7ed0cd5db152e25#p44824

DonH50 · Jan 1, 2013

I don't have an account (and no real desire, don't have enough time now for various fora). Phase noise on the clock is applied to every signal so I assume that is what they are describing. I am thinking of a way to show this in spectral plots, and thus create a file one could listen to for such jitter...

jkeny · Jan 1, 2013

DonH50 said:
I don't have an account (and no real desire, don't have enough time now for various fora).

I know that feeling

Phase noise on the clock is applied to every signal so I assume that is what they are describing. I am thinking of a way to show this in spectral plots, and thus create a file one could listen to for such jitter...

No, where that particular text I quoted came from was after a repeat of the Hawksford experiment run on an eMu soundcard

At this point I have tried to repeat exactly the Hawksford experiment, that is, playing back a pure 1kHz audio tone, at different levels, and register the jitter spectrum -if generated? - for each one, concentrating only for the in-band, audio products.
Here it is, in a downwards -decreasing order: 1kHz, -3db green,
-20dB okker,
-40dB red,
-60dB viola,
-70dB dark green.

The last, -70dB d.green track is superimposed on the red track - lack of space...

As You see, there IS a lot of jitter generated, as the audio signal level is decreasing. While at -3dB we see practically zero, at -70dB the peak level is ~28psec jitter, with a long series of harmonics. Of which the second is always missing, in a good agreement with Hawksford. 28psec is Twice the amount of peak jitter that was generated by the Hiface, before mod!
At only -20dB we already have 8psec peak jitter.

jkeny · Jan 1, 2013

So one of the many interesting things on that thread I referenced is that extract & graph - as the signal level decreases the jitter level increases. This is perhaps one of the many reasons behind the oft quoted view that one of the flaws of digital audio is it's worse resolution at low level compared to analogue - just as level goes down & we need better resolution, jitter goes up & small signal distortions are even more pronounced.

Audibility of Small Distortions

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