You’re not alone… They aren’t for me either. But I do know a few people that like them.
Perhaps a different way of thinking about it. The example given is at a frequency of 1/4 the sample rate. If there were ANY deviations from a sine at 1/4 the sample rate there would have to be higher frequency harmonics of the signal, but even just the 2nd harmonic would be 1/2 the sample rate, the others would be higher, none of which can happen if the original signal was bandlimited to less than 1/2 the sample rate. There’s only one possible sine that goes thru those samples and any frequencies higher would have been filtered out when the signal was originally digitized.
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This last explanation is very helpful for me.
I don’t know why I didn’t start there 
I have a lot of shortcut ways of thinking, and without a lot of explaining, at times, they don’t seem well founded to the casual observer.
Still the pictures above show how bad no filter is for high frequencies at 44.1k and that upsampling (perhaps even without much of a filter) gets a lot closer to the original signal.
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It’s important to remember that “what sounds good” is entirely subjective. There is no universal truth. It’s all dependent upon the tastes of the one doing the listening.
It becomes dogmatic when you make definitive statement like the one above. Instead of “this is bad” and “this is good”, a more accurate statement would be “I, Mr. Smith, like this” and “I, Mr. Smith, don’t like that”. Expanding that out, fans of DS/J products like this, but don’t like that.
That’s far different than decreeing “this is good” and “this is bad”. It’s similar to decreeing that only white rice is good. White rice is best for those that like white rice. Yet white rice is not inherently, cosmically, or universally better. Nor is any one approach of digital to analog conversion inherently better. It’s subjective.
Like most of you, I’m a music and music equipment explorer. On the equipment side, I really enjoyed my over 2 years with the DSJ. I have nothing but respect for it’s reproduction of music. It was time for a change, so I just sold it. Now I’m exploring the R2R NOS tube avenue of D to A conversion. And one day I’m sure I’ll get bored with it, and switch to whatever else looks interesting at the time.
The grander point being, no matter our DAC preferences, can’t we agree upon the spirit of adventure and exploration that this hobby provides? This is truly the golden age of DAC options on the market. And China is coming on strong with a new wave of affordable, high quality products. It will be interesting to see what the future holds. If China can produce high end gear at a fraction of the price, I wonder how PS Audio and other USA based companies are going to compete?
No, I’m just correcting some of your many misstatements. You are the one saying things like
That is clearly false as I have shown. I’m not going to bother chasing all of your misinformation down, just enough that people can clearly see that you are just playing the victim and not a technical guy. Nothing wrong with not being technical, most people aren’t technical and live life just fine. The difference is that most people don’t try to defend false technical statements to the death.
I thought it was obvious that I was using “good” and “bad” as descriptions of the fidelity of the output to the input. Not some value judgement about people that like one kind of sound or another or about the value of a DAC.
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I think your last abstract (and the prior explanations) perfectly show that it makes no sense to try to construct technical explanations, argumentations or justifications out of personal listening preferences, especially when having no clue of even basics (which is normal for most of us pure music listeners). A personal listening preference stays what it is as well as technical superiority can still mean, that some prefer the sound of technically clearly limited designs.
What I can say is, that my personal DAC history from that first TDA1541 design, over a 1Bit design, then as they said “world’s first upsampling CD player” and then other better upsampling designs, I can definitely confirm your illustrations from my experience that this first upsanpling DAC was the first more or less natural sound experience from CD. Still very compromised in PRAT, frequency extremes and other characteristics, but much better than the early designs before. One of the latest players was more than double the price of the DS. Still any of even those latest designs had obvious flaws for me, even without direct comparison to better sources.
The DS sr. then, since decades of experience with different, older DAC designs, was a much bigger change than everything before and the first digital source for me, that had no shortcomings anymore while listening to it, unless directly compared to few multiple times more expensive sources.
This characteristic of not letting me miss anything and not noticing shortcomings anymore when listening to a digital source without further comparison, was an essential experience for me and kept me satisfied since years now.
This story is why I was so surprised that there are NOS DACs available, still inheriting (a certainly improved in its periphery) basic chip design with the same basic limitations I used 30 years ago.
Since a while my impression is, that some, with digital try to reach a certain characteristic of bad turntable sound, while great turntable sound and great digital sound get quite close with modern DAC designs. That doesn’t mean, reaching great turntable sound is a goal of digital at all, it’s certainly not. Both just try to get closer to the optimum from different sides.
Would you say this is only a problem for normal folks trying to understand things, or that also among DAC designers, wrong information and conclusion is used?
So, are more or less all DAC designers understanding things the same way and just try to reach their best (or fulfilling listener preferences) by different approaches…or are only some using correct basics (still by different approaches)?
Once again, thanks very much @tedsmith. Reading through your explanation, this is the “magical step” that I can’t grasp “that changes all of the zeros to the samples that would have to been there if the analog input was antialias filtered at 1/2 the sample frequency”.
in my vast ignorance (I am a lawyer with rudimentary calculus education), I always thought that the upsampling was done by interpolation, and that the “new” samples would add the "volume"bits determined by the interpolation algorithm. In your example, it would add 146 16/24bit words, as determined by the algorithm. I had no idea that the upsampling was done by adding zeros.
I think I can understand the benefits of upsampling, using a less severe digital filter to remove out-of-band noise, trying at best to preserve sine wave bandwidth at least to 20khz. But this adding zeros really got me head over feet.
Thanks for bearing with an uneducated laymen.
It puts me in mind of taking a nasty low res 1 bit monochrome document scan, switching it to 256 greyscale, and “blurring” it - which makes it much more readable and fills in the nasty white gaps where edges of letters should be 
Most designers aren’t designing DACs from first principles: for example the DAC chip has already made a lot of these decisions. Even so, many amateur DAC designers make mistakes when doing the analog filters… Most people that have had college courses in digital signal processing understand this stuff, but still some argue about the more subtle details. The deeper details like how reality differs from the ideal repeating waveform usually used in analysis or how to choose the best kernel filter for antialiasing or reconstruction is confusing to many, but those differences are still small compared to what happens when just skipping the filter or skipping upsampling.
Yes, but there are a lot of interpolators: some much worse than others. Here’s a thread about this:
https://forum.psaudio.com/t/upsampling-oversampling-smooth-or-stairs-curve-between-values-determiniation/5791?u=tedsmith
Blurring is a low pass filter function. That’s exactly what’s going on in audio too.
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Thanks for all of your time here Ted! Even though there may have been a few shortcuts here and there, I think you’ve done one heck of a job explaining these concepts. You could maybe call my understanding of digital signal processing surface level, even so, I feel I can follow your explanations reasonably well.
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Maybe time to close this thread.
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It must be fascinating to work in this complex world of electronic design, informed by a lot of experience aside of school books, and then suddenly (or maybe as a matter of consequence) good sound results (on a very different level of real life experience)! Must be as if a physicist’s work creates a symphony.
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Aloha @tedsmith
This is actually much easier to understand than you’re making it.
What sounds best, the best sound, is exclusively determined by the ears doing the listening. What qualifies as the “best sound” is an entirely individual determination.
If the Ted Smith / Benchmark DAC approach of lower noise and upsampling sounds best to an individual, then that’s the best sound - for them. If a R2R NOS sounds best to an individual, then that’s the best sound - for them. If a person prefers a $100 boom box, then that’s the best sound. Etc, etc…
The “best sound” is not determined by software programming calculations. A computer does not get to decide what sounds best. What sounds best is determined by millions and billions of ears, all with different preferences.
Therefore, the dogmatic belief that “lower noise always creates better sound” is a fundamentally false statement. This is not about engineering, it’s about human perception.
A more truthful statement would be “lower noise may create better sound quality”. Changing “always” to “may“ yields a far more truthful statement. A far less dogmatic statement.
Bringing it back down to my personal experience. My DAC journey went from a $300 PeachTree Audio DAC, to a SGCD, to your DSJ. I liked all three for different reasons. Windom represented a lowering of noise compared to Snowmass. I much prefer Snowmass. Therefore to me, the lowering of noise yielded lower sound quality.
That alone strikes down the theory that lower noise “always” creates better sound. The fact that I found Windom lacking means “lower noise always sounds better” is a false statement. The “always” part makes it untrue.
This truly has nothing to do with engineering or programming, or even hardware. It entirely revolves around personal preference. Beauty is indeed in the eye of the beholder.
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Lower noise = more detail and therefore closer to the “truth”. The truth being the holy grail of hi-fi. Hi-fi meaning High Fidelity.
Perhaps lower fidelity sounds better to you. Nothing wrong with that. But Ted’s job and PS Audio’s aims are for higher, not lower fidelity.
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we had a similar disconnected debate in a preamp thread a couple of months back.
define sound quality.
-
most engaging, most enjoyable, most emotional connection to the music.
highly dependent on the listener, allows for all sorts of differences between input and output if that produces the desired effect in the listener. -
output signal is closest to the input signal.
measureable, and calculable in the case of a dac.
@dancingsea - i think you (inadvertently, i hope) do Ted a disservice by arguing (1) when he is clearly explaining how to achieve (2).
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If you enjoy R2R NOS DACs, at least go for the best one. It is Burr-Brown’s PCM1704 and/or one of the premium hand trimmed variants. Wadia, Linn, Meridian, Naim & Resolution Audio all used them.
Hi Ted. You mentioned that 512 DSD is possible with the Direct Stream Dac, but that it will probably never happen. Is that written in stone, or will it be sometime in the near future? I know you are quite tied with the Obsidian, but if it can be done, I think many will appreciate it.
Doing twice as much work in the same time probably isn’t possible. I have done parts of it but it either requires a clock faster than the FGPA supports or doubling the real estate needed for upsampling and doing the sigma delta modulator. There are other uses of those resources which will bring more sound quality improvements.
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