Delta Sigma: An Inconvenient Truth

Discussion in 'Digital: DACs, USB converters, decrapifiers' started by k4rstar, Jun 21, 2020.

  1. skem

    skem Friend

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    @Serious, I agree with all your points.

    The “edginess“ of higher-order crossovers is probably what I am referring to. See, for example, comments by people converting Troels’ ellipticor-3 first-order crossovers to one with higher slopes for better “dynamics” despite the first-order version having “electrostatic-like” speed from the Scanspeak drivers. Equally I have speakers with both 2nd order crossovers (with flat-ish F.R.) and no-crossover widebanders (with shit F.R.). The widebanders sound better for well mic’ed recordings of instrumental music.

    I agree also that some headphones count as fairly coherent, especially planars, and it’s why I like them. I was under the impression that all dynamic drivers had some phase shift—am I wrong here? In any case, still better than speakers. That’s actually a big part of why I hang around SBAF. That and the haute-culture company that this place attracts.

    I can’t argue decisively for or against linear-phase filters. You’re right that the group delay is *mostly* constant over the pass band, but how much dispersion is allowed in the definition of “mostly”? It’s certainly not the case that oversampling DACs don’t have timbre or stage; they do! It’s that NOS DACs seem to do it even better, and I was theorizing that the reason might be the smaller phase shifts from the gentler analog filters. We can hear remarkably small levels of nonlinear/harmonic distortion at THD=0.05%, so why not also remarkably small phase shifts on key overtones? I don’t know; I’m offering this as a theory, not gospel.
     
    Last edited: Jun 29, 2020
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  2. RobS

    RobS RobS? More like RobDiarrhea.

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    What I like about you skem is how much of a timbre fantatic you are. What's the best DAC you've heard for timbre?
     
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  3. skem

    skem Friend

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    Metrum Adagio, of course.
     
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  4. purr1n

    purr1n Finding his inner redneck

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    You should hear a few NOS DS DACs, of which a few do exist. I think what you are attributing to NOS is more Metrum's sound rather than NOS.

    The phase shifts are worse on 44.1kHz NOS with steep filters.
     
  5. skem

    skem Friend

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    @purr1n, if I had the access to gear, I’d totally do this comparison. I am deeply curious what makes these things sound so different.

    If not NOS, what do you think is responsible for Metrum’s sound?
     
  6. purr1n

    purr1n Finding his inner redneck

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    The cook is responsible for Metrum's sound. Heck, even the Amethyst, Onyx, Pavane, Adagio, sounds different from the first gen Metrum Hex and Octave.

    Even then, the cook may have had a goal in mind based on something else he may have tasted, say to the capture the sound of the TDA1541, UltraAnalog, PCM54, etc. of long ago, but put his twist on it.
     
    Last edited: Jun 29, 2020
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  7. skem

    skem Friend

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    I like Cee's cooking, but I'd still like to know the magic ingredients that make it sound as it does. A dash of R2R, a drizzle of NOS syrup? Wherein lies the secret to the secret sauce. Or is this really architecture independent, like Nelson and his tedious transistor-screening habits?
     
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  8. crenca

    crenca Friend

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    This is a strange attribution of subjective (i.e. you feel it "gets old") quality to objective engineering and what is simply math that is as you admit "necessary" for any sound to be reproduced from digital sampling at all. Do you feel the calculations necessary to build a bridge that does not collapse "gets old", or that the wheel nut torque required to keep your wheels on your car "gets old"? Rhetorical question of course.

    The gentle/slow low pass used in a typical DSD implementation has very minimal phase shift fuckery as I understand it, and DSD (due to it's very high sampling rate, and its inherent low pass reconstruction "filter") has no pre/post "ringing". How these facts are correlated to subjective stage and imagine perception is I suppose the question in any particular piece of gear.

    In my opinion, there seems to be and underlying confusion of the general relationship of frequency and time domains in waveform reproduction with circuit implementations (DS, R2R, etc.) behind much of the discussion on this thread...
     
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  9. k4rstar

    k4rstar Done his time

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    I don't really understand your question or analogy. I was talking about the perceived subjective effects of the objective engineering decisions. In that sentence the perceived subjective effects, whatever they may be, are what gets old.

    could you provide some resources or further insight to educate us, I would appreciate it
     
  10. crenca

    crenca Friend

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    Except that you do not actually link the objective engineering with the subjective. How for example is oversampling (however it is implemented in a real world circuit) in the digital domain related to phase in the passband? You simply assert that it is, an assertion that is not based on the actual math (unless I am in error).

    Related to the above, it's the bit depth and not sample rate/over sampling that is directly related to the time domain (i.e. "phase"):

    https://troll-audio.com/articles/time-resolution-of-digital-audio/
     
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  11. purr1n

    purr1n Finding his inner redneck

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    I don't think it's that easy. To really grasp this stuff, a strong background in numerical analysis would be needed. To start, there have already been several fundamental misunderstandings: forgetting that there is also an analog filter which is separate from the digital filter embedded in the upsampling or "oversampling" algorithm. Or thinking that somehow noise shaping or approximation has no place in PCM (of which R2R is the native architecture). The Internet is the worse place to understand this stuff. A entire book can be written about this. @ultrabike and I have better things to do.
     
    Last edited: Jun 29, 2020
  12. m17xr2b

    m17xr2b Friend

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    Penguins might as well speculate about nuclear physics and me along side on how a DAC filter works.
    Bits go in, magic happens and spits out music, I could care less about anything else since it won't tell me how those differences correlate to the sound of different architectures, or how I'm going to benefit by understanding the maths apart from a super high level for a generic approach since most cool stuff is hidden.
    Typical D/S - loses some music info still major debates on how much
    Yggdrasil burrito - doesn't lose info still not perfect
    Metrum - FPGA or whatever, yummy tone, less intrusive, who knows what's wrong with it

    It's all academic and isn't worth getting upset about. Meets is how this is going to be resolved, multiple people with different tastes listening to the same gear, debating impressions then sharing.
    Otherwise it's like trying to describe a colour, others say it's different yet it would be so much easier if we looked at it. Too much orange turning into pink and name calling over it.
     
    Last edited: Jun 29, 2020
  13. Hands

    Hands Overzealous Auto Flusher - Measurbator

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    I believe Cees usually follows a few common design principles with his DACs:

    1. High slew rate I/V (Pavane specified at 1500V/uS)
    2. High bandwidth I/V (Pavane specified at 500MHz)
    3. Mild analog filter (Pavane specified with only a 1st order filter at 70KHz)

    But a lot of technical specifics are under wraps, literally and figuratively, so it's hard to say much beyond that. He seems to like paralleling a lot of DACs at least, and they're some sort of multibit architecture. I believe even in his DAC ONE and TWO modules, he isn't using discrete resistor ladders, but some IC or combination of ICs.

    If you primarily use SE outs, you'll also hear influence based on his common choice of Lundahl transformers in the higher end DACs.

    There's a lot of subjective marketing fluff in this, most of which is also covered in some white paper Cees put out a while back, but it does go over his design goals and line of thinking: http://6moons.com/audioreviews2/metrum/1.html

    Even going back to his earliest products, speed, bandwidth, and general analog stage simplicity have been common themes (or claims). In that link above, one claim is that such speed and bandwidth will cause measurably worse jitter via the JTest method, and that a more normal I/V stage produces more normal results. Basically a, "Well, it measures worse, but I think there's something to extreme speed and bandwidth that sound better." sort of thing. Probably a feeling we can all relate to in some way, whether or not we agree.

    I'd wager the speed, bandwidth, and relatively simple output stage principles play a decent role in the Metrum/Sonnet DAC hosue sound, with the varying DAC ICs/modules and evolving digital logic filling in the gaps.

    Then again, I've done direct A/B testing of a DIY NOS AD1862 DAC against the Pavane (first gen). The former is pretty much in-line with a lot of textbook and datasheet designs, down to the I/V and output stages, both of which are opamp-based. And it sounds strikingly similar to the Pavane...so...Who knows?
     
    Last edited: Jun 29, 2020
  14. purr1n

    purr1n Finding his inner redneck

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    ^ Well spoken.

    Mainly because it surmises on the why without getting heavy on it. Once things get heavy, it get's bullshitty for variety of reasons: 1) we simply don't know - there's a lot we don't know and will never know because it's sound - not railguns or nukes; 2) it's parroted stuff from manufacturers claims; 3) it's parroted stuff from the Internet; 4) people without serious math and engineering chops aren't going to be able to get it quickly - there is a ton of stuff that isn't intuitive - like WTF we would need to reconstruct a signal, HTF we would handle quantization error (can't map real-life into a tidy set of integers), or HTF one-bit can even work, etc.

    Let me add one to the top:

    Vinyl - by all measures, total shit, but sounds better with older music because an unneeded AD-DA screws something up?
     
    Last edited: Jun 29, 2020
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  15. RedFuneral

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    Does this mean I may have been enjoying my NOS DACs because they ring & are phasey while sitting on a high horse of time domain superiority? That would be amusing but it would mean I spread a bit of misinformation over the years. :eek:
     
  16. crenca

    crenca Friend

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    At least you're able to admit it.

    For years I was convinced that "Hi Res", PCM > than 16/44.1, had more "resolution" (more perfectly re-constructed the wave form) in the audio band. Not that "Hi Res" can't help from an implementation standpoint (from either a sampling or bit depth point of view), but given how trivial oversampling is today, Hi Res is 99.99% audiophool marketing.

    Maybe to slightly disagree with @purr1n, I wonder if non math people (aka, 99% of audiophiles out there - including myself as it has been 30 years now since I passed a calculus class) could not benefit by taking the time to understand the implications of Nyquist–Shannon, even if the math is always going tooto be out of reach...
     
    Last edited: Jun 29, 2020
  17. monacelli

    monacelli Friend

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    I understand where this sentiment is coming from, but I'm frankly not sure how helpful it would be. As Papa Pass likes to say, "It's entertainment, not dialysis." The math behind digital audio is beautiful, but has extremely little bearing on the way audiophiles experience their music. The Nyquist-Shannon sampling theorem itself just says that given an *ideal* reconstruction filter, it is possible to precisely reconstruct an analog signal with a maximum frequency of B (Hz) given only a digital version of the signal sampled at 2B (samples per second). Does knowing that make your DAC sound any better? Does not knowing it make your DAC sound any worse? D/S DACs wouldn't measure so well if they didn't get the fundamental facts right. But given the number of audiophiles who proclaim to hate the sound of D/S DACs, it's obvious that raw technical accuracy is not enough to satisfy the human ear. It seems that this concept of pulse width modulation, which underlies switching power supplies, delta-sigma DACs, and class D amplification, can affect human perception in ways that are difficult to quantify. But the reason these technologies often produce unsatisfactory aural experiences cannot be attributed to poor measured performance in the audio band, or to some endemic failure by the engineers. So we're left with personal preference, and our ears as our most trustworthy instruments to determine good from bad. The thing this thread is sorely lacking is actual impressions. "I like this because of [X]." or "I can't explain why, but I'm unmoved by [piece of gear Y]." Infinitely more useful than looking awkwardly at each other and mumbling something about Claude Shannon.

    If there are folks who are genuinely curious about the math and have at least a little background, these are two of the most-cited classic papers:
    • R. W. Schafer and L. R. Rabiner, "A digital signal processing approach to interpolation" [pdf here]
    • C. Shannon, "Communication in the presence of noise" [pdf here]
     
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  18. purr1n

    purr1n Finding his inner redneck

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    This is the easier version: https://en.wikipedia.org/wiki/Whittaker–Shannon_interpolation_formula

    Homework for tonight:
    1. In Excel, write a function that outputs the samples of a 15kHz sine wave at 44.1kHz
    2. Note how the samples, the dots, look like WTF, and nothing close to s sine.
    3. Implement a sinc interpolation function to reconstruct the 15kHz sine, no need to do n=-∞ to +∞. Something like n=-5 to 5 actually gets us very close. (Obviously, recreate the signal at a much higher sampling rate so we can actually visualize the 15kHz as a sine.)
    4. Wonder at the magic
    Extra credit:
    1. Do the above, but make each sample fit into a 16-bit Integer via rounding (actually make it 6-bits to make it press the point).
    2. Realize with horror at the errors, the approximations. This is quantization error.
    3. Implement a dither (noise) formula that reduces harmonic distortion from the quantization error at the expense of higher noise floor.
    Extra-extra credit

    Shape the noise so that most of it is tilted above 10kHz​
     
  19. will_f

    will_f Friend

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    Speaking as a math person, I’d say no unless someone has a strong interest in building a DAC. Much as I find the hardware reproduction aspect of music fascinating, I have no intentions of building any hardware and am happy to accept the idea that some engineers are just better at their jobs than others.

    Math is a big world with a lot of beautiful parks to explore. A good book on our current understanding of quantum physics or modern acoustical engineering would be my recommendations. Add probability theory for those that like to gamble.
     
    Last edited: Jun 29, 2020
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  20. spwath

    spwath Collegiate hijinks master

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    Did part 1:
    upload_2020-6-29_23-15-13.png

    Tried upping sampling rate
    upload_2020-6-29_23-15-38.png

    Upped it even more
    upload_2020-6-29_23-15-56.png

    Then tried really low sampling rate and got... odd results. Looks more like 1000 hz than 15kHz.
    upload_2020-6-29_23-16-19.png

    Anyway, ill try the other parts tomorrow. Seem more complicated...


    EDIT: I realize what went wrong with that last graph. Its the graph type I chose. If I just chose dots, it would be more accurate. Should not connect the dots there.
     

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