Chord Mojo(1) DAC-amp ☆★►FAQ in 3rd post!◄★☆
Apr 16, 2016 at 12:26 PM Post #16,099 of 42,765
That must mean something.

 
Are you sure?
 
LOL
biggrin.gif

 
Apr 16, 2016 at 12:34 PM Post #16,101 of 42,765
  Looking for some advice, I currently have Mojo and ie800s, and am looking for full size headphones.
 
Considering HD650, HE-400i and AQ Nighthawk.
 
Which would compliment mojo best ?
 
 
Thanks

 
My HD 650s soundstage is good, bottom end a bit congested, upper and mids crisp. the bottom end congestion could be due to the music choice, because it is occasionally and only with heavily layered tracks
 
Apr 16, 2016 at 1:34 PM Post #16,102 of 42,765
Hey there,
I am curious to find out which efficient 8 ohm horn loudspeakers Rob was talking about.
I am also interested in other suggestions for hornspeakers, including DIY sets.
Cheers
 
Apr 16, 2016 at 2:15 PM Post #16,103 of 42,765
  The Mojo outclasses the Theta in upper frequency details. No doubt, the Mojo is more accurate with better decay and textures in the upper end. This is very slight, but noticable. Also, the Mojo sounds better than the Theta when playing back anything 24-bit. I downsample all my 24-bit music to 16/44.1khz when I listen to my Theta. There is simply more detail when listening to hi-res music through the Mojo versus the Theta.

 
Now here is what surprised me. CD quality/Redbook sounds as good if not better than the Mojo when played through the Theta. Now that I think about it, the Theta was designed with only that level of quality in mind so it should sound better with CD quality considering the DAC designers have forgot what the late 80s/90s were all about.


That might one explanation. But I think something else may be going on. Mike Moffat has mentioned on several occasions that Schiit's filter is a closed-form upsampling algorithm, i.e. a "real-time high-res converter". This means that when you stick redbook 44.1 kHz material into the Theta, it will spit out an exactly estimated high-res version of the input.
 
My understanding is that Chord's math, while a better implementation than the traditional successive-approximation used in DS chips and keeps the original samples, it still falls short of a being a closed-form solution. Which means that while the Mojo will do upsampling, it will feature a degree of approximation in the output.
 
I think this might partly explain why Theta does better than Mojo with standard redbook material...
 
Apr 16, 2016 at 2:30 PM Post #16,104 of 42,765
 
The Mojo outclasses the Theta in upper frequency details. No doubt, the Mojo is more accurate with better decay and textures in the upper end. This is very slight, but noticable. Also, the Mojo sounds better than the Theta when playing back anything 24-bit. I downsample all my 24-bit music to 16/44.1khz when I listen to my Theta. There is simply more detail when listening to hi-res music through the Mojo versus the Theta.
 
Now here is what surprised me. CD quality/Redbook sounds as good if not better than the Mojo when played through the Theta. Now that I think about it, the Theta was designed with only that level of quality in mind so it should sound better with CD quality considering the DAC designers have forgot what the late 80s/90s were all about.



That might one explanation. But I think something else may be going on. Mike Moffat has mentioned on several occasions that Schiit's filter is a closed-form upsampling algorithm, i.e. a "real-time high-res converter". This means that when you stick redbook 44.1 kHz material into the Theta, it will spit out an exactly estimated high-res version of the input.

My understanding is that Chord's math, while a better implementation than the traditional successive-approximation used in DS chips and keeps the original samples, it still falls short of a being a closed-form solution. Which means that while the Mojo will do upsampling, it will feature a degree of approximation in the output.

I think this might partly explain why Theta does better than Mojo with standard redbook material...


What has "closed-form" got to do with anything?

https://en.wikipedia.org/wiki/Closed-form_expression

Is there such a thing as an "open-form upsampling algorithm"--seeing as "not closed form" means "not computable by any means"? :rolleyes:

What is "an exactly estimated high-res version of the input?" Is it an estimate, or is it exact? For it to even be an "estimate" there needs to be e.g. blind spectral band replication applied from under 22kHz to over 22kHz:
https://en.wikipedia.org/wiki/Spectral_band_replication

The amount of calculation needed for this is simply not something you can put in the kind of CPU a Schiit uses. Is there even any hint that the Schiit puts out calculated harmonics at higher frequencies than that allowed by the input material's sample rate? :rolleyes:

And an "exact estimation", if such a term even means anything, I suppose means it can exactly recreate the high frequency content of the high-res master from the CD material. Which is even more ridiculous.

But I have no horse in this race. Judging from the drivel Rob and Mike each put out, Chord and Schiit really deserve each other as competitors. :rolleyes:
 
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Apr 16, 2016 at 2:44 PM Post #16,106 of 42,765
What has "closed-form" got to do with anything?

https://en.wikipedia.org/wiki/Closed-form_expression

Is there such a thing as an "open-form upsampling algorithm"--seeing as "not closed form" means "not computable by any means"?
rolleyes.gif


What is "an exactly estimated high-res version of the input?" Is it an estimate, or is it exact?
And an "exact estimation", if such a term even means anything, I suppose means it can exactly recreate the high frequency content of the high-res master from the CD material. Which is even more ridiculous.
 

 
I will not be getting into a fist-fight on this, but here are some elements:
- "closed-form" means that the algorithm estimates a single, unique solution using exact, deterministic math. Most delta-sigma implementations will rely on successive-approximation techniques when upsampling (i.e. Parks-McClellan), so discarding the original samples and re-estimating them using algorithms relying on approximations. So, to make this very clear: closed-form unique solution vs numerically approximated solution
 
- of course you cannot recreate the high-freq material. That would be ridiculous. What you can do however is obtain more data-points along your recreated waveform (not least to avoid aliasing distortion). To obtain these extra data-points DS approaches will again rely on successive-approximations, whereas Schiit's algorithms seems to obtain exact solutions (while retaining all the original samples). Chord seems to be using some approximations, but still retain the original samples. DS approaches don't.
 
If you're genuinely interested in these things (and not stirring waves and insulting people just for the fun of it) then take a look at Lavry's white-paper on digital sampling, esp. p.26. You get the same notions, but the other way around:
 
HTH
 
Apr 16, 2016 at 2:49 PM Post #16,107 of 42,765
- of course you cannot recreate the high-freq material. That would be ridiculous.


As I pointed out, you can actually attempt to recreate the high-freq material. It's just obviously outside the means of any Schiit DAC, even though they would like you to think they're doing something special to make CDs sound like high res.
https://www.google.com/search?q=blind+spectral+band+replication&ie=utf-8&oe=utf-8#
 
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Apr 16, 2016 at 2:55 PM Post #16,108 of 42,765
"closed-form" means that the algorithm estimates a single, unique solution using exact, deterministic math. Most delta-sigma implementations will rely on successive-approximation techniques when upsampling (i.e. Parks-McClellan), so discarding the original samples and re-estimating them using algorithms relying on approximations. So, to make this very clear: closed-form unique solution vs numerically approximated solution


The fact that you preserve the original samples as a precondition obviously doesn't make your interpolated samples any more accurate than any other method. If Schiit had somehow managed to create a filter that does mathematically perfect upsampling using the puny resources of a portable DAC, well, they should be patenting this, taking it to NASA and revolutionizing orbit calculations for spaceflight, weather forecasts or something, I dunno, anything would be better than trying to sell audiophile DACs.
 
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Apr 16, 2016 at 3:48 PM Post #16,109 of 42,765
Actually I think I may have fallen into a trap here.

Preserving the original sample points when upsampling, in a non-cheating workflow, would imply having a perfect brickwall filter of infinite length as the interpolation filter. Because otherwise there's simply no way the resampled audio can naturally pass through the original sample points.

IF (and that's a big IF) the megaburrito filter actually does what it claims, short of pulling an infinite computing miracle, it can only do this by bending the interpolated points toward the original sample points in a non-optimal manner.

This can be demonstrated using Audacity and Adobe Audition:

1. Here, a Dirac impulse drawn on silence sampled at 44.1kHz, shown in Audacity which does not perform any interpolation in its display (or, strictly speaking, "linear interpolation"):


As you may know, a Dirac impulse contains all frequencies theoretically encodable by the format, so this is a real test of resampling.

2. Here, the same impulse as interpolated by Audition in display. It has to show the original sample points where they are, so there's your megaburrito filter! :ph34r:

See how the interpolated curve passes through all the original points (i.e. all on the middle line except for the impulse in the middle)? Is this really the ideal resampling we're all looking for?

3. I perform offline resampling of the track using the following settings which I believe to be optimal for the present application. Feel free to correct me:


4. The result. Note that the original sample points are NOT on the middle line anymore. (they're close, really quite close, but no cigar.) If keeping the original samples were desirable, why would Audition do it for the real-time visualization but discard it for (supposedly highest quality) offline rendering?


Note also that the pre / post impulse waveforms undulate for further before and after the impulse. You may know this to be a sign of a resampling filter that's closer to ideal, as a mathematically ideal filter would cause the impulse to pre-ring and post-ring for infinite time. (not that this is a bad thing, because proper music samples ought to have all frequencies so close to the transition band filtered out during recording analog-digital conversion.)

To summarize, the fact that
1. Adobe Audition uses a "megaburrito" filter for real time visualization but not high quality offline conversion, and
2. The offline conversion shows characteristics of a higher quality conversion despite not looking like a "megaburrito" filter

Speaks volumes about the actual desirability (or not) of preserving the original samples in integer-multiple sample rate conversion.

Then again, AFAIK no one has actually been able to tap the internal upsampled digital stream of a Schiit DAC for analysis, so who knows if it actually preserves the original samples? :rolleyes:
 
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Apr 16, 2016 at 4:03 PM Post #16,110 of 42,765
Actually I think I may have fallen into a trap here.

Then again, AFAIK no one has actually been able to tap the internal upsampled digital stream of a Schiit DAC for analysis, so who knows if it actually preserves the original samples?
rolleyes.gif

 
so are you trying to say Mike Moffat and crew are damn lucky, or outstanding mathematicians?
 

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