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Thread: Audible Jitter/amirm vs Ethan Winer

  1. #101
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    Quote Originally Posted by amirm View Post
    Jitter creates unwanted harmonics. Once those harmonics rise up to the same level as what a single bit of audio sample would represent, then you would lose that bit of accuracy.
    Ah, okay, then I withdraw my withdrawal. Or, I was right the first time. Since jitter level is related to the signal level, then a very soft passage has jitter that is also very soft. So turning up the volume past normal will not make the jitter audible because it's still 80 to 120 dB below the music.

    You can't on one hand say that 14 bits is good enough for some music but not for other
    Sure I can! And you even agreed with me. With typical pop music that's normalized nobody can ever hear jitter or dither or using "only" 14 bits. I bet even 12 bits would be fine, other than maybe during a very quiet part. That's about what you get from good analog tape or LP records.

    --Ethan

  2. #102
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    Quote Originally Posted by DonH50 View Post
    Random jitter does not create harmonic distortion; it creates spurs in the response but these are somewhat randomly related to the signal. Deterministic jitter will create harmonic distortion terms.
    That is correct and was the topic of my first few posts here . But since jitter doesn't have to be random, we need to look at all of its modes and I described the common ones we worry about in audio circles as a simplification.

    Quantization noise is not harmonic distortion of the signal, but rather more like, well, noise! It sounds worse than thermal noise because it is not truly white noise and there is a relationship to the signal. INL can (and does) create harmonics.
    That's not correct Don. Quantization noise is not "noise." In signal processing circles, we use the term noise to describe distortion and harmonic distortion is exactly what we have here. This is easy to show, starting with stealing graphs from this well written little article on the web (there are countless others -- this is my first hit): http://www.cadenzarecording.com/Dither.html

    Here is a picture of what happens if you just truncate 24 bits to 16 bits:



    We see what appears to be square wave overlaid on our original signal. How do you make square waves? Well, with odd harmonics of a signal! We can see this in his simulations of a 100 Hz in 24 bits first before truncation:



    Now after truncation to 16 bits:



    If you look at the horizontal axis you see that the first harmonic peak created as a result of truncation is at 300 Hz. The next one is at 500 Hz. The one after is at 700Hz and so on. It clearly follows the pattern of odd harmonics (3, 5, 7, etc.).

    Let's add a bit of (simple) dither to it and this is what we get:



    Miracle happens! We add noise to the signal *before* conversion from 24 to 16 and now all the distortion is gone and replaced with noise. For once, math is behind you when it comes to audio fidelity .

    OK, so there is no free lunch. You get elevated noise floor. Let's overlay the before and after dither:



    Fortunately there are clever techniques such as "noise shaping" to remove the audible impact of such noise. But that's for another chapter .

  3. #103
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    I know this is about jitter, but since you posted graphs of how dither helps, I'd like to say I clearly remember some photos (not graphs) you once posted that clearly showed the effect of dither. A picture tells as much as a thousand words I have heard.

    Pity you could not come up with those pics again, or indeed a similar pic which shows jitter (for those reading, I mean an actual photo of something, not graphs etc)

  4. #104
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    We'll have to agree to disagree on this one, Amir. For the theory, look at something like Discrete Signal Processing by Oppenheim and Schaffer (pretty sure that's the one -- mine's at work). I do believe ideal quantization generates only odd-order terms, but of course there are other things at play, e.g. the relationship of the clock to the signal, that causes every bin to fill in even in an ideal system. That's why the usual white-noise approximations are valid and standardly used. (Standardly, is that a word? I be an engineer, not a grammar person...) To me, noise and distortion arise from different things in the circuit, and have a much different impact on the output. I do not treat them the same. Maybe that's one difference between us low-brow hairy-knuckled engineers and the high-brow scientist types, but it's in me blood.

    Truncation to 16 bits is not the same as sampling with a 16-bit system; truncation will add distortion. In that paper, I think dither is primarily masking the truncation errors, and you need a goodly amount of energy to that, thus the relatively high noise floor. Dither normally only needs to be a few lsbs, raising the noise floor by only a few dB, unless there is a lot of nonlinearity. At least, that's the way on works in the systems I have worked with (audio and RF, though we play other games in the RF world to decorrelate the spurs and not raise in-band noise). If I ever built a 16-bit converter with that high of spurs (only 40 dBFS or so, about what you might get out of 5 to 6 bit converter), I'd be fired, or at least tied to my desk until I fixed it. Maybe I should run some plots to show the differences, hmmm... In any event, the paper is an interesting and useful look at the impact of dither, but the test case is unrealistic. I suspect something else is going on...

    Also, the impact of noise decorrelation (dither) is a bit different in delta-sigma designs (which I assume is the architecture you plotted from the rising noise response) than in a conventional converter. The early 1-bit, low-order loops were very prone to tones and dither was (and is, for that matter, in any such loops) required to suppress tones in the output of the delta-sigma modulator (ADC or DAC). Technology and techniques have advanced so that modern architectures are more complex, higher-order and often using multi-bit loops, so dither is less critical for stability and tones, though is often still added to produce a more pleasing noise floor.

    To address your first point last, we agree on that one! That's why I am (usually) careful to distinguish between random and deterministic jitter. And, though I have yet to really research it in depth, I still feel deterministic jitter is a far worse culprit that random jitter for us (no matter what frequency we operate).


    Back to practicing - Don
    Don Herman
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  5. #105
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    terryj -- Virtually all test systems now are computer-based so actual photos using film are almost impossible to come by, and you'll be taking a picture of a digital display anyway. Maybe if we dig up some vintage test equipment (we have some in our lab, but I'm not sure it still works). However, there are pix around showing the effect on musical spectra, if that helps... By "photos" do you mean time-domain pictures instead of spectral (frequency domain) plots? - Don
    Don Herman
    "After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
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  6. #106
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    Those pictures were sure a hit, weren't they.

    So here is a set of pictures I have to show jitter.

    First without any jitter:



    Now let's see what happens to it when we apply the kind of jitter Ethan says is not audible:



    Case closed. No?

    OK, so here is a less silly demonstration by stereophile magazine: http://www.stereophile.com/features/1208jitter/



    Real jitter will look worse than above because its motion is not uniform across the image as the above image represents. But then again, its magnitude would be less.

  7. #107
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    And, now you know why we musicians just ignore the ape with the stick up front...
    Don Herman
    "After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
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  8. #108
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    Ashkenazy seems to need a new razor. The reviews of his latest Exton release of the Respighi Pines of Rome, Fountains of Rome, and Feste Romane might suggest that he was in a bit of simian-mode, though.

    Overall, this is one of the best audio threads ever. Great work, guys.

    Lee

  9. #109
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    When in Rome... Actually, we might be due for Pines again this fall, thanks for reminding me of yet another thing I need to practice before the season starts!
    Don Herman
    "After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
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  10. #110
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    Whilst piddling I made a few plots that y'all might find interesting...

    First is a plot showing the aperture time for various ADC or DAC resolutions vs. signal frequency. The aperture time is the time required for the signal to move 1 lsb, assuming a sine wave. If the jitter equals the aperture time, you lose about 8 dB in SNR assuming normal random jitter.

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    To see the impact of jitter, let's look at a 16-bit converter sampling at 44.1 kS/s (CD resolution and rate). The DAC is perfect except for the added random timing jitter. A perfect 16-bit ADC has SNR of about 98 dB. I have plotted the SNR vs. jitter for 100 Hz, 1 kHz, 2 kHz, 10 kHz, and 20 kHz signals. You can clearly see how the higher frequencies are much more sensitive to jitter. At 100 Hz, 10 ns of jitter is hardly noticeable, but at just 1 kHz the SNR has decreased by nearly 20 dB (down about 3 bits)! At 20 kHz, we have SNR less than an ideal 10-bit DAC (< 60 dB).

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    Another way to look at the impact is to plot the SNR lost as jitter increases, as shown below. A perfect 16-bit DAC would lose 0 dB in SNR; as jitter increases, more and more SNR is lost. With 1 ns of random jitter, things don't look too bad through 2 kHz, but at 20 kHz we see that 20 dB SNR loss.

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    To keep the loss to just a few dB at 20 kHz, we need jitter < 100 ps; with 1 ns the upper midrange and high end is getting pretty noisy, with the effective dynamic range reduced by 10 to 20 dB...

    Fun with plots, hope this helps - Don
    Don Herman
    "After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
    Don's Technical Articles on WBF

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