Review and Measurements of Chord Mojo DAC and Amp

[iAmMathew]

I think the official site states their measurements are at 3V output (you just press volume buttons together when mojo powers up). I have read on head-fi, that Rob Watts prefers optical input, since optical is immune to RF noise. Could you redo the sinad measurement at 3V and with mojo's optical input (dog eyes)?

 

[Veri]

I think the official site states their measurements are at 3V output (you just press volume buttons together when mojo powers up). I have read on head-fi, that Rob Watts prefers optical input, since optical is immune to RF noise. Could you redo the sinad measurement at 3V and with mojo's optical input (dog eyes)?

He no longer has a Mojo for testing it was a loaner.

 

[vkvedam]

Hi Amir, have you thought about measuring it via Toslink or SPDIF?

 

[amirm]

Hi there. I don't have it anymore to test differently.

 

[Stan Smitchen]

Compared to my lg v30 and FiiO E10K Olympus 2, the Chord Mojo seems to me the worse choice . I ordered fortunately with amazon, so the return was only a formality.

I can not hear barely a difference. And not as practical as I imagined. The cable connection to the smartphone is absolutely ... "no can do". And after no more than half an hour, the Mojo runs really hot.

I have the following headphones in use: Sennheiser hd 660s / 700 / momentum 2 wired, inear stagediver sd2.

chord electronics... it smells like snake oil?

 

[VintageFlanker]

chord electronics... it smells like snake oil?

It's not. The Mojo provides very respectable performance measurements-wise for a portable unit. The debate is more focused about the price/performance ratio. There are more competitive products out there.

The Mojo, still, is way more powerful than either your V30 or E10K...

 

[Stan Smitchen]

Unfortunately, this additional power makes no sense. I can neither hear it nor profit from it.

 

[Simon P]

I have heard Chord DACs but not in my own system.

Rob Watts points out quite rightly IMO that the elephant in the room with digital audio is that there has always been a lot of carelessness and presumption regarding the time domain accuracy performance. This is not snake oil, it is measured time domain performance compared to an ideal filter satisfying the relevant criteria. Because a very loose approach to implementing the reconstruction filter in terms of time domain impulse response will still yield superb frequency-phase-sine wave reproduction, and because these are the traditional measurement parameters, engineers have simply disregarded the rather poor time domain behaviour.

The whole digital audio scenario is framed by the Shannon-Whittaker-Nyquist theories. These require a perfect fd brickwall and the corollary in the time domain, a perfect sinc impulse response. In reality you can't get either, but the frequency domain issue has been the one focused on almost exclusively. Most engineers have neglected the td response and accepted a -50dB or so accuracy with it. They'd never do that for a traditional frequency domain measurement. Until a short while ago those were the only figures published, leading some to say that digital audio was a fully solved problem.

I'm wondering how Watts sees the legitimacy of time-asymmetric impulse response filters. These seem to me to have very little to do with accurate reconstruction of correctly digitised signals. They may possibly sound good, but not because they are likely to represent more nearly correct reconstruction of the filtered ADC input.

 

[dc655321]

Most engineers have neglected the td response and accepted a -50dB or so accuracy with it.

What is the "time domain response" you are referring to and what is it -50dB relative to?

 

[Soniclife]

Most engineers have neglected the td response and accepted a -50dB or so accuracy with it. They'd never do that for a traditional frequency domain measurement.

Do you have any measurements or links to measurement that show this?

 

[Simon P]

The fact that conventional digital audio is based on sinc (sine x/x) function impulse response is, I would think, beyond dispute. There's a Wikipedia entry for the Nyquist-Shannon Theorem which corroborates this; see the last but one paragraph of the introduction. There's a link further back on this thread to an article by Keith Howard describing the thinking behind the Chord approach to filters which starts by setting out this aspect of digital audio. It includes a representation of the sinc function in time and shows the number of sampling intervals against the value of the function scaled linearly and in dB. To represent the sinc function in time with the same sort of accuracy reserved for DA conversion itself requires the sort of tap lengths used by Chord.

Basically this is overlooked, without, as far as I can see, clear justification. If it can be shown that truncating the sinc function in the usual way actually does not produce significant errors on a music waveform when compared with a much more nearly-correct sinc function implementation, then all of this is indeed irrelevant.

It may be Chord have decided there has been an excess focus on frequency-phase domain performance, SNR and maybe clock jitter, in an unbalanced way for the goal of optimum overall performance.

 

[dc655321]

There's a link further back on this thread to an article by Keith Howard describing the thinking behind the Chord approach to filters which starts by setting out this aspect of digital audio. It includes a representation of the sinc function in time and shows the number of sampling intervals against the value of the function scaled linearly and in dB. To represent the sinc function in time with the same sort of accuracy reserved for DA conversion itself requires the sort of tap lengths used by Chord.

Ah. Your comment, "Most engineers have neglected the td response and accepted a -50dB or so accuracy with it", statement is referencing Fig 5 here? Not sure how you arrive at the interpretation of that as -50dB error. Perhaps you could explain?

Basically this is overlooked, without, as far as I can see, clear justification. If it can be shown that truncating the sinc function in the usual way actually does not produce significant errors on a music waveform when compared with a much more nearly-correct sinc function implementation, then all of this is indeed irrelevant.

The longer the sinc function, the sharper the transition band. Trading off filter length for a somewhat less steep transition band and still maintaining adequate image rejection is a common engineering compromise. Going too far with the compromise could lead to problems, of course. I'm sure there are examples on this site of good and bad implementations. For example, this was looked at in some detail in ASR's review of the Chord Mojo.

If the recordings you listen to are properly band-limited, I would not be too concerned about what my DAC is doing in the vicinity of 20kHz or above.
Unless you're a bat...

 

[amirm]

Rob Watts points out quite rightly IMO that the elephant in the room with digital audio is that there has always been a lot of carelessness and presumption regarding the time domain accuracy performance.

Time domain accuracy is not important at all. In real life you get reflections from sources of sound which come at different times than the original sound. If we were so sensitive to time, we would go crazy. Your speakers by the way create such time non-linearities more than anything else. See: https://www.audiosciencereview.com/...d-measurements-of-jds-labs-el-dac.4850/page-2

I know of no study remotely that backs what Watts is saying here. He himself performs sighted tests on his own work which in my view and that of science, is worthless. If all of this is audible and backed by objective science, then he should run a formal listening test and prove it. Instead, when I asked him if he believes in blind tests, he said no as they confuse people or some such response.

 

[Simon P]

The longer the sinc function, the sharper the transition band. Trading off filter length for a somewhat less steep transition band and still maintaining adequate image rejection is a common engineering compromise. Going too far with the compromise could lead to problems, of course. I'm sure there are examples on this site of good and bad implementations. For example, this was looked at in some detail in ASR's review of the Chord Mojo.

If the recordings you listen to are properly band-limited, I would not be too concerned about what my DAC is doing in the vicinity of 20kHz or above.
Unless you're a bat...

There are several things to discuss here. Better sinc function equals better brick wall, yes. Perfect sinc equals perfect brickwall with infinite stopband attenuation. The basic thing being questioned by Rob Watts of course is how sinc implementation affects the true time-wise amplitude reconstruction accuracy, rather than phase-amplitude plots in the frequency domain. Implicitly we are discussing the relative importance of timewise reconstruction vs. phase-frequency measurements. Filter design has used the latter as its starting point, hardly surprising as the Nyquist criterea starts with a frequency domain constraint, and that is how audio engineers have come to think; there being no great potential in analogue systems, in the linear region, for time domain problems not reflected in frequency domain measurements. Digital is potentially and probably IMO another story. Watts clearly thinks so.

Second, the actual filters used to approximate correct ADC anti-aliasing and DAC reconstruction are many and varied. Not all are closely based on a sinc function time domain result anyway.

To essentially re-state, the DAC filter can be seen as an anti-imaging filter or a reconstruction filter. In reality it is both. Both functions are potentially important. The first has had the emphasis in engineering thinking, historically.

Third, then, and most relevant here, is that the superposition of sinc functions at the sample rate is only perfectly accurate if that sinc function continues indefinitely in time both ways. I'm assuming, as Keith Howard was, that the DAC filter is indeed based on a sinc or very similar td function. Anything else is only a loose attempt to fulfil the Nyquist-Shannon reconstruction criterea, although it may have merit. For truncated (real world filter) sinc, reconstruction will be entirely accurate at precise sample time, but will be inaccurate, by a complex function, and to a degree not easily determined, at times other than precise sample times. The Keith Howard article explains the essence of this well.

The whole issue shows that digital audio will never be absolutely perfect and never can be. It is rather about 'how close can it be?' and 'how close is it now?', 'what would possibly improve it further in current practice' and 'is it good enough for your purposes now?'.

 

[Simon P]

Time domain accuracy is not important at all. In real life you get reflections from sources of sound which come at different times than the original sound. If we were so sensitive to time, we would go crazy. Your speakers by the way create such time non-linearities more than anything else. See: https://www.audiosciencereview.com/...d-measurements-of-jds-labs-el-dac.4850/page-2

I know of no study remotely that backs what Watts is saying here. He himself performs sighted tests on his own work which in my view and that of science, is worthless. If all of this is audible and backed by objective science, then he should run a formal listening test and prove it. Instead, when I asked him if he believes in blind tests, he said no as they confuse people or some such response.

Hi Amir. Speakers make simple distortions. Digital makes more complex distortions not found in simple natural phenomena like acoustics. That is a common and reasonable line of discussion, it seems to me.

Watts thinks long taps makes a difference; I can see he may have a technical point. Consensus only takes you so far. I'd actually like to listen more carefully myself.

 

[dc655321]

The whole issue shows that digital audio will never be absolutely perfect and never can be. It is rather about 'how close can it be?' and 'how close is it now?', 'what would possibly improve it further in current practice' and 'is it good enough for your purposes now?'.

Digital audio today can be audibly perfect, and that is what counts - not adherence to the absolute mathematical ideal.

Rob Watts is good engineer and Chord make good, if expensive, products. But, when he talks about the audibility of effects at -300dB (that's 10^-15) or -170dB, his credibility among peers goes out the window. Not only are those numbers irrelevant physiologically, they're irrelevant electronically/technologically too. Perversely, among people who know no better, such talk helps his bottom line...

The basic thing being questioned by Rob Watts of course is how sinc implementation affects the true time-wise amplitude reconstruction accuracy, rather than phase-amplitude plots in the frequency domain. Implicitly we are discussing the relative importance of timewise reconstruction vs. phase-frequency measurements. Filter design has used the latter as its starting point, hardly surprising as the Nyquist criterea starts with a frequency domain constraint, and that is how audio engineers have come to think; there being no great potential in analogue systems, in the linear region, for time domain problems not reflected in frequency domain measurements.

Not sure what this incoherent bit is intended to convey.
The time and frequency domains are very intimately related - they cannot be decoupled as you seem to think.

 

[pkane]

The time and frequency domains are very intimately related - they cannot be decoupled as you seem to think.

I see this claim made a lot in the audiophile circles. There is no such thing as a time-domain only error. Any error in the time domain has a corresponding error in the frequency domain.

 

[Simon P]

Not sure what this incoherent bit is intended to convey.
The time and frequency domains are very intimately related - they cannot be decoupled as you seem to think.

Not sure what is incoherent there.

I personally have not heard Watts talk about -300dB or -170dB and neither would bother me.

As I understand it he's talking about inter-sample interpolation amplitude errors potentially reaching levels of up to -50dB or so of digital full scale, in a way that is a very complex function of analogue input signal. You have not suggested a reason why he is wrong.

TD and FD cannot be decoupled, you're right. They are related by Fourier transform. But the relationship between them for minor deviations from perfect implementations, and that is what we are all looking at in audio with sought accuracies of 30ppm or so with thd plots for example, is not at all simple. In particular, the interpolation aspect can potentially throw up substantial errors. If I can get my hands on Matlab I may get round to doing some models.

We are talking about extremely small discrepancies in FD having relatively larger amplitude-at-time discrepancies in non-repeating music files. They are conjugate variables; a small FD error may give a large time error and vice-versa. This is an aspect of Fourier uncertainty.

Nothing you have said so far alters my perspective on this, so far. There will be errors, and they may be quite large by normal audio measurement standards.

The proof of the pudding will be a representative simulation and/or a time aligned reconstruction of the same sound file made with different sinc based reconstruction filters compared in analogue. And whether those differences, and they will be there, are considered audible by various people.

 

[dc655321]

As I understand it he's talking about inter-sample interpolation amplitude errors potentially reaching levels of up to -50dB or so of digital full scale, in a way that is a very complex function of analogue input signal. You have not suggested a reason why he is wrong.

If it takes you 5 posts to explicitly state what you're concerned about, that is incoherence.

"Inter-sample overs" can certainly be a problem. They're introduced in the recording process and neglected in the reproduction chain. Of all the dsp ills that Rob Watts proposes, I don't recall him calling out this problem explicitly (doesn't mean he hasn't, of course), or framing his sales pitches in terms of offering a solution for that problem.

He could just recommend, "trim source volume by 3-6dB", but that would produce insufficient mystique...

In particular, the interpolation aspect can potentially throw up substantial errors. If I can get my hands on Matlab I may get round to doing some models.

The proof of the pudding will be a representative simulation and/or a time aligned reconstruction of the same sound file made with different sinc based reconstruction filters compared in analogue. And whether those differences, and they will be there, are considered audible by various people.

Or, you can just take a look for existing research. This is not new territory.
But, please do explore. Maybe start a new thread on the issues and your findings?

John Siau: https://benchmarkmedia.com/blogs/application_notes/intersample-overs-in-cd-recordings

@amirm - the "acid test" in the following Reddit link may be interesting to add to your repertoire (full-scale at fs/4, sounds similar to J-Test)

https://www.reddit.com/r/audiophile/comments/7akd5k

 

[amirm]

Hi Amir. Speakers make simple distortions. Digital makes more complex distortions not found in simple natural phenomena like acoustics. That is a common and reasonable line of discussion, it seems to me.

Hi there. We measure distortion and with DACs, they can incredibly low amount of it. Few amplifiers can keep up with them and fewer speakers can do the same. Indeed DACs are pushing the limits of what we can measure as far as distortion using audio analyzers.