Delta Sigma: An Inconvenient Truth

@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.

 

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?

 

Metrum Adagio, of course.

 

@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?

 

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?

 

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...

 

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

 

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/

 

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.

 

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.

 

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...

 

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]

 

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.

 

Did part 1:


Tried upping sampling rate


Upped it even more


Then tried really low sampling rate and got... odd results. Looks more like 1000 hz than 15kHz.


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.