DEMO / MUSINGS: Let's listen to some jitter simulations with sideband distortions...

A couple weeks ago, we started getting into the topic of jitter and the concept of whether jitter is audible and at what level. As I had expressed at that time, my belief based on experience with the equipment I have looked at / listened to is that with almost any reasonable modern day digital audio device, the likelihood that one would hear sampling jitter effects is extremely unlikely. No need for crazy expensive cables that claim jitter improvements. No need for high-priced servers (like this), expensive streamers, or "de-jitter"/"reclock"/"regen" devices. But one of course does want to have a good DAC with excellent jitter rejection, and these days, competent asynchronous USB devices almost universally will achieve excellent results by reducing jitter from the interface (remember, the older S/PDIF digital interfaces typically perform worse than modern USB or ethernet even though newer devices like the Oppo UDP-205 perform excellently with any of the inputs).

The reason I say this comes not just from measurements and my own listening to devices with different severities of sampling jitter, but also experimentation over the years in simulating the distortions introduced by jitter.

As I mentioned last time, with Yamamoto2002-san's WWAudioFilter, we can easily use DSP to introduce fixed amounts of sinusoidal periodic jitter to "bake in" the kinds of sideband anomalies often found with devices that suffer from jitter. For today's post, what I want to do is provide some test files you can use to actually hear what severe jitter distortions with sideband anomalies sound like. Think of this post as similar to one years ago when I demonstrated what poor USB cables sound like.

Furthermore, coming out of this article, I hope the audiophile reader can appreciate the magnitude of jitter that is necessary in order for the effect to become audible. In so doing, I hope it will help us appreciate the results from the J-Test FFT's I publish here and also when you look at measurements elsewhere (like on Stereophile).

First, remember that jitter is a complex phenomenon with many potential forms. A "primer" on the subject can be found from Silicon Labs describing jitter in devices of much higher operating frequency (MHz and GHz) than just the audible range. Consider for example the diagram at the start of the "primer" describing the "classes of jitter" we can think about and how they might manifest in our audio systems.

Remember that jitter is a timing anomaly and multiple elements can either cause or contribute to this abnormality as discussed in that PDF. Back in the old days, analogue timing anomalies in the form of "wow and flutter" were much easier to hear and describe because typically the variation is of low frequency and leads to obvious pitch fluctuation or "wobble" to the sound. The ease of hearing this is probably why there's less controversy; once you hear it and know what it is, we can all just talk about it without there needing to be any lack of clarity about the phenomenon. Digital sampling jitter however is different. Jitter effects obviously exist in the DAC's analogue output but the tiny timing inaccuracies from crystal oscillators affect higher frequencies more severely (where auditory acuity is not as sensitive) and the frequency anomalies show up in a much subtler way than slow wobbly frequency shifts off vinyl playback for example (we can easily measure this wow & flutter anomaly as previously discussed).

In the audiophile world, the J-Test we commonly see in measurements is based on Julian Dunn's work from the early 1990's created to measure the AES3 (adopted for S/PDIF coaxial or TosLink) digital interface jitter (see the linked paper for rationale around the test development). While not a S/PDIF-based device, as an illustration of what it typically could look like, here's a J-Test result from 2013 taken from an old 2008 15" MacBook Pro's headphone output:

The diagram above is a typical 16-bit Dunn J-Test. One of the give-aways is that with a low enough noise floor, the jitter-modulation tone which is a 225Hz square wave in the LSB (least significant bit) shows up as a harmonic sequence as you can see with the numerous peaks to the left used to stimulate jitter abnormalities. Also, 16-bit J-Tests have the primary signal sitting at 11kHz (whereas the 24-bit J-Test based on 48kHz sampling rate has the primary signal at 12kHz).

At the base of this J-Test primary signal is the "skirting" often talked about. This potentially represents some low-level timing imperfection showing up as noise. Perhaps with a higher resolution FFT, we can zoom into those frequencies and make out the difference between periodic jitter presenting as tiny sidebands as compared to random jitter with a typical Gaussian distribution. Remember also that the measurement system has some intrinsic jitter that can contribute to this (the FFT above was captured with my old E-MU 0404USB and the AKM AK5385a ADC chip). On either side of the primary signal for this MacBook Pro at +/- ~2.2kHz in blue, we see a pair of "jitter modulated sidebands" which are likely the result of periodic jitter which includes "sinusoidal" jitter owing to the undulating shape of the subtle timing irregularity.

Notice I also have a yellow question mark on the graph. We don't see a clearly elevated mirror spike on the other side of the primary signal to suggest the presence of a sideband pair. This could be "periodic spurious noise" or a "spur" likely correlates to something in the computer's circuitry. I'd need to go back to the MacBook Pro and examine when this noise shows up to understand whether this is some kind of constant noise related to the computer's components or perhaps jitter at a single offset frequency triggered during playback.

Having said this... Since most of the time, jitter (like for the MacBook above) presents itself strongest as sidebands, the question obviously is - "what do these jitter-modulation sidebands sound like"!? To answer that question will allow us as audiophiles to take a step forward in being able to perhaps identify the effect in our hi-fi systems when we hear them, and also consider whether descriptions by others such as equipment reviewers actually could be attributable to jitter effects. For example, I've heard audio reviewers claim that things like "three-dimensionality" deteriorates with jitter, or that jitter "reduces the air" around instruments, maybe "changes the timbre of sounds", or "blurs the transients". Are these descriptions really what jitter - specifically jitter-induced sidebands - do to the sound of actual music?

Let's cut to the chase. Using WWAudioFilter, I created files with simulated jitter sidebands to listen to. I used a number of samples to show off variations depending on the underlying signal / music. Here are 4 sets of audio files (archived as RARs - 13-115MB) for you to download, listen to, and consider.

1. 20-20kHz Sine Sweep Jitter Test - as the name implies, this is a simple sine sweep from 20Hz to 20kHz over 30 seconds.

2. Schubert String Jitter Test - 90 seconds excerpt downloaded from 2L Hi-Res Test Bench of "Schubert String Quartet No. 14 in Dm", performed by the Oslo String Quartet (from The Schubert Connection). I downsampled the 24/96 file to 24/44.1 prior to employing the DSP processing.

3. Piano Improvisations Jitter Test - 90 seconds excerpt downloaded from 2L Hi-Res Test Bench of Ola Gjeilo's "Piano Improvisation" (from Piano Improvisations). I also downsampled the 24/96 file to 24/44.1 prior to employing the DSP processing.

4. London Nights Jitter Test - how about non-acoustic studio productions? Here's a test set using a pop/disco recording from 1989 :-). This is 90 seconds of London Boys' "London Nights" (DR10, from The Twelve Commandments of Dance). This recording is from the 16/44.1 CD rip run through the DSP to 24-bit output prior to dithering.

As usual, I provide these short musical excerpts under the provision of "fair use" for the purpose of education, research, and discussion. If you enjoy the music, buy the recordings!

When you open each of the RAR files, you will see each set consists of 10 "versions", each with a certain total number of nanoseconds of sinusoidal jitter distortion applied. To manage file size, I dithered the 24-bit output down to 16-bits; trust me, you don't need 24-bits resolution to hear the magnitude of the effect being introduced. I have checked the files to make sure that the DSP did not overload and add distortions. To give you a visual sense of the amount of distortion I've applied to these test files, let me run through each setting used and show the severity of sideband distortion using the 16-bit J-Test FFT as graphed using Adobe Audition CS6 (65536 bins).

A. No simulated jitter added (0ns)

No sinusoidal jitter added:

DSP settings for WWAudioFilter.

16-bit J-Test (16/44) full spectrum FFT.

Notice that although no jitter distortion was added, I ran the file through WWAudioFilter anyways to make sure the DSP program did not affect the audio data. As expected, no sidebands introduced.

B. 0.875ns (875ps)

Before talking about nanoseconds even, let's start with a few hundred picoseconds of cumulative sinusoidal jitter "baked in". While I'm taking some liberties and simplifying things, this level of sideband distortion from sampling jitter is around the order of magnitude of some relatively poor quality CD players and DACs. If we look through Stereophile reviews over the years, we see some machines with cumulative jitter sideband anomalies similar in value or a little higher - Esoteric SA-60 from 2007, Emotiva ERC-2 in 2012, Philips CDR880 CD-R/RW recorder in 1998, Burmester Reference Line 970 DAC & 969  CD Transport from 1999 . This level of jitter is in fact considered "moderate" already with digital players. Most CD players actually measure below a cumulative 400ps when Stereophile was still using the Miller Jitter Test to calculate a number (for example, here's the Squeezebox Transporter - estimated between 235-313 ps only).

For these simulations, I've chosen to create 3 sideband pairs for you to listen for. +/- 225Hz which is not uncommonly seen in many devices. A +/- 1125Hz pair. And then finally a pair +/- 2475Hz which is similar to what we saw with the MacBook Pro above. Notice that the strongest amplitude pair is the most proximal and it decreases going outwards. This is often what we see with actual equipment measurements. Of course, these frequencies are nonharmonic tones of the primary signal.

The most prominent sidebands are at an amplitude of about 92dB below the primary 11kHz peak. As you can imagine, this is very low amplitude and I'll leave you to mull over whether you believe your ears/brain would be able to hear this at normal volumes and of course listen to the music and sine sweep and decide for yourself. For completeness, also do not forget the importance of masking; those +/-225Hz sidebands would likely be much more difficult to hear than then +/-2475Hz pair.

Finallly, remember that at this sub-nanosecond level of simulated jitter, your playback equipment could hypothetically exacerbate the effect if your DAC introduces its own significant amount of timing inaccuracy.

C. 3.5ns

Compared to essentially all DAC or CD players out there, this would be quite severe jitter sideband distortion.

The amplitudes of the sidebands are -80dB below the peak signal in the proximal pair and -90dB for the pair ~2.5kHz away. We have seen inexpensive Walmart-consumer-level devices like this "lo-fi" Sony boombox perform at around this level of distortion on J-Tests.

By the way, one of the worst performing devices over the years in Stereophile was the Zanden 5000 Mk. IV/Signature which measured a cumulative value of 4.4-4.9ns - just a bit over the amount here. Another device recently measured with sidebands of this magnitude appears to be the Aqua Formula xHD (NOS, R-2R DAC, remarkably poor technical performance for 2018!) with sidebands down around -80-90dB range using the 16-bit J-Test.

D. 17.5ns

Getting more intense now with stronger sidebands. Again, if we look at the 16-bit J-Test results from actual DAC and CD players, this amount of sideband intensity is very strong! I would imagine only some of the very worst devices could even "hope" to approach this level of temporal inaccuracy.

E. 175ns

And it gets worse! The sidebands are now intense enough to "spill over" to involve other frequencies beyond the 3 pairs (these are called "second order sidebands"). The strongest sidebands +/- 225Hz are now just about -40dB below the primary signal peak.

F. 875ns

Okay, now we're getting really serious :-). Just shy of 1 microsecond (1000ns) of cumulative jitter among the sidebands. Only -32dB between the primary 11kHz peak and the strongest +/-225Hz sidebands with 500ns in that component alone. Looks really scary and bad...

G. 1750ns

Okay, another jump. Now we're at almost 2 µs of cumulative sinusoidal sampling jitter added by the 3 DSP filter actions! Seeing much more spill over and frequency effects. Hmmm, how bad does this sound?

H. 8750ns!

Ugly folks. Almost 9 µs equivalent worth of sideband distortions across the audible spectrum. By this point the strongest sideband amplitude is only about -12dB down from the primary signal. I don't think anyone would be surprised that the effect on music fidelity will be strong.

I. 17500ns!!

Arrrrgggggghhhh... Anomalies present essentially across the audio spectrum now!

J. 35000ns!!!

The worst audio system ever type of distortion by this stage! Simply a brutal, noisy mess with a total of 35µs sinusoidal jitter simulated by the DSP filter operations. Although the frequencies are still "centered" around the 11kHz primary signal, notice that the 11kHz tone amplitude in this test signal itself has been eclipsed by the sideband amplitude. I'm obviously pushing the distortion to extremes here for demonstration.

So... What does this sound like?

That is the obvious first question to ask yourself when you listen to the simulated jitter samples:

- How would I use words to characterize the effect?
- Do the typical audiophile adjectives referring to things like "3D soundstage", "veil", "blurring", "dynamic range", "resolution", "air", "presence", "noise" apply?
- Do I notice a difference in quality depending on the type of music and instrumentation?

The second obvious question then is - "At what level of simulated sinusoidal jitter severity do I start hearing the abnormality?"

- Can I already hear it at the lowest 875ps level?
- It looks pretty bad already when I look at that 17.5ns J-Test FFT! How bad does it sound when listening to the music?
- Can I hear a difference between headphones and speakers?
- If I were to blind test or ABX these files (like using foobar ABX comparator), at what level would I confidently hear a statistically significant difference?

For me, I cannot hear a difference with the 875ps or 3.5ns cumulative distortion tracks even though those first couple steps already incorporate more sideband distortions than the vast majority of devices I've come across! Sitting at my computer, with Audio Technica ATH-M50 closed headphones or 1MORE Quad Driver IEMs using my ASUS Xonar Essence One DAC, the lowest level where I could reliably hear the anomaly with the 20-20kHz synthetic sweep test is the 175ns sample. (Haven't tried with my Sennheiser HD800 yet, but will at some point.)

As for the real musical samples, for me, the effect is different with each of the tracks... For the "Schubert Strings" track, I notice a slight "nervousness" with the sound of the high frequencies and a "grittiness" starting at 875ns which progressively gets obvious. I found detecting the anomaly more difficult with the "Piano Improvisation" sample on my headphones (a bit more reverb to the track masks the distortion). What I did notice by 1750ns was a gradual deterioration of the piano decay with a "hardness" to the sound and this became very noticeable of course by 17500ns and 35000ns where the "dysphonic" fuzziness exerted themselves strongly!

For "London Nights", the first few notes (Big Ben quarter bells chime) provided an opportunity to hear the distortion. Remember that digital sampling jitter manifests more strongly in the higher frequencies. For me, those synthetic bells in the pop/disco song were subtly affected by the 875ns sample and became obvious by 8750ns with the harsh overtones. Once the song gets going with all kinds of sonic layers, the distortion became more difficult to tease out although it should be evident here and there throughout the song obviously once we hit the 17500ns sample amount.

The fact that the abnormalities can be heard easily at 175ns with the synthetic sweep while needing higher values like 875ns+ with real music is not surprising. Recordings have a higher noise floor, and when distortions fluctuate like these sidebands depending on the signal, we can appreciate them much easier with simple test signals where we can predict the sound (whether single tone or sweep) and "lock on" to anomalies.

What has always struck me, not just here with these samples but over the years as I have listened to other tests of jitter is simply how much is required before I can put my finger on the distortion. For me, it certainly isn't at the level of a cumulative tens or hundreds of picoseconds as typically found in decent digital gear. Instead even with synthetic tests at normal volumes (the 20-20kHz sweep test is very annoying at higher volumes), I need something like 100ns using the frequency distribution of the sidebands used here to appreciate the distortions! Needless to say, this level of jitter distortion is orders of magnitude worse than the vast majority of CD players and DACs out there.

Conclusions

Well, I hope you have fun with these test samples and take the opportunity to play around with WWAudioFilter yourself (excellent work Yamamoto-san). Try it out with your own music, maybe using other settings for the frequency of the sinusoidal jitter added. Remember that a larger frequency displacement (like +/- 5kHz) from the primary signal will make the distortion more audible but this is rather unusual for real equipment. Typically, I've seen sidebands show up less than +/-4kHz on either side of the J-Test primary signal.

A few summary points then:

1. You can now say that you have an idea of what periodic jitter that causes sideband distortions as shown on J-Test FFTs sound like. Remember that there are other jitter-related effects and the sonic anomaly will change depending on the sideband frequencies. Random jitter can elevate the noise floor potentially globally but also in a Gaussian distribution. Single spurs are also possible with certain DACs and equipment.

2. You've now also heard the effect not only with a test signal but with actual music. The effect varies depending on the audio signal and I think you can appreciate that the subjective nature of the jitter distortion is a bit different between the string orchestra, to piano, to pop music. Related to this is that if music is poorly recorded with low dynamic range and high noise floor, you're probably unlikely to hear jitter distortions at all even if high. This latter point is why I used the old pop/dance tune "London Nights" (DR10) from 1989 rather that typical DR6-level dynamic compressed modern masterings.

3. Speaking of sideband intensity, remember that for digital sampling jitter, higher frequencies are affected more. You can see this if you look at the FFT of the sine sweep sample as it moves from low to high frequency and the increasing level of the sideband "lobes" in relation to the steady primary signal amplitude:

This is probably another reason why it can be hard to "pin down" what jitter "sounds like". Also, because jitter affects higher frequencies more, as we get older, the high frequency sideband may be less noticeable as high-frequency hearing acuity decreases for us guys especially.

4.  You've now also experienced the magnitude of effect that is required to make the distortion audible. This is perhaps the most important point in this whole exercise. For me, even with a synthetic sweep, it took >100ns of cumulative sinusoidal jitter in the frequencies used (+/-225Hz, +/-1125Hz, +/-2475Hz distribution with decreasing amounts for each as above) before I could hear distortion! This is obviously a level of sideband distortion significantly beyond what we see with CD/DAC measurements. As I said a couple weeks ago, finding jitter distortion is certainly not impossible out in the wild... But it will be like looking for the giant panda. You'll only rarely find it when you know where to look.

Over the years, I have discussed my suspicions about devices like "regenerating" USB hubs, "purifiers", passive filters, doubts about digital cables of normal length supposedly capable of reducing jitter, and I've read articles from folks who seem to find (and hear) jitter everywhere! The designers and manufacturers have had every opportunity to demonstrate that these devices are able to do something to improve sound quality. The fact that they don't show objective results for their products and in fact essentially ignores calls to produce evidence when confronted is telling (time for the snake oil detector to trigger!).

I trust that after listening to these test files and reviewing the graphs, it's not hard to understand why I have a hard time getting too excited (worried?) about jitter these days with decent digital audio gear. Obviously, I want equipment that reproduces the audio to have minimal distortion and ideally engineers should be striving for jitterless DACs. As we've seen recently with measurements of the Oppo UDP-205, we're already at a level that IMO no human being could complain about with good gear at reasonable prices! Beware of unnecessary fears, uncertainties, and doubts published in the "high end" consumer audiophile world to perpetuate the scary jitter boogeyman and attempts at selling equipment to ward off this apparition.

One last thing. Because humans are subjective creatures with idiosyncrasies, realize that it is possible that jitter might actually "add" to the sound quality and be subjectively preferred by some. For example, the limitations and distortions of LP playback are probably why some (many even) folks like the "analog" sound. As I mentioned above, there are a few digital devices like the Zanden DAC and certain NOS R-2R DACs that perform relatively poorly in regards to jitter. Another device like this would be the Audio Note NOS CD players. I think it's worth considering whether a higher but not extreme level of subtly audible jitter may add to why some audiophiles prefer the sound of these devices. While not technically ideal, nor "high fidelity", the distortions could be "euphonic" to some. Of course, I have never come across anyone agreeing to such a thing - after all, who wants to admit that they actually like the sound of jitter distortion!? :-)

BTW: If you want to read a good research paper on jitter audibility, have a look at this one from AES 1998: Benjamin & Gannon "Theoretical and Audible Effects of Jitter on Digital Audio Quality". Thresholds of audibility in the review are in the tens to hundreds of nanoseconds with more sensitive test material, better with trained listeners (no surprise).

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Behold! In house now. Pillar hardware for the Archimago's Musings' "Generation 3" audio testing. :-)

We'll talk about this soon.

Have a great August, everyone... Hope you're enjoying the music!