NDX and Chord Hugo

The Naim Dac oversamples to 768 Khz from a 48Khz (CD quality) recording. Most DACs use oversampling it is not particularly unique in this regard.

There are 1,000,000 microseconds in one second.

768,000 / 1,000,000 = 1.3 microseconds.

Therefore the oversampling in the Naim Dac creates a sample every 1.3 microseconds. Well below the 4 microsecond threshold that I have read is claimed as the point at which human hearing can establish separation of timing.

Incidentally, this threshold is widely held to be much, much lower at about 10-30 milliseconds i.e. 30/1000 (thirty thousandths) of a second not 4/1,000,000 (four millionths) of a second. This by sources such as Yamaha Pro Audio and hearing-aid manufacturers who presumably know a thing or two on this subject.

Naim have previously stated the main purpose of oversampling in the case of DACs is to make it easier and hence cheaper to remove the high frequency artefacts which DACs introduce without resort to costly analogue components and engineering.

The smoothness of the curve resulting (as an approximation of the smooth analogue curve) may be a red herring as clearly you can get a completely smooth curve by joining-the-dots on 48,000 points in representation of as small a timeframe as one second. If you're unsure about this, it may be proven at home with a very fine nib and several days to spare.

One other thing to remember is that Naim and most other contemporary DACs throw away the extra samples created in oversampling. They were simply a means to an end (on aspect of conversion from digital to analogue). They do not represent smoother lines or more detail. They are not presented to the listener when the music emanates from the speakers.

Exactly right Mark.  The early CDs had what they called 'Brick Wall Filters' and I believe the earliest were centred at the Red-Book sampling rate of 44.1kHz.  These approximations to a 'Brick-Wall Filter' produced all sorts of ringing right into the audio band.  So 4-time oversampling became the norm at (4 * 44.1)kHz.  Shift the sampling frequency up from 4-times and the filters you use can be a much more gentle affair and any artefacts that are produce should not intrude into the audio band

Did the single bit, 'Bitstream' DACs do oversampling - not sure to be honest.

You have to remember that when our square waves are converted to analog the very process will 'smooth out' the analog produced.   So I have never been sure if interpolation is viable anyway.  I also think that if you do it then you would do the interpolation in the digital domain, difficult to do maths in the analog domain.

To generate any sort of stepped waveform in the analog domain will contain lots of high frequencies, so the filtering we spoke of will remove this and smooth out the waveform.  If you look at a square wave on a scope you will see that the corners are curved not sharp.  You can produce a square wave on a computer by adding together a sequence of sine waves:

Fundamental +

3 times the frequency at one third amplitude +

9 times the frequency at one ninth amplitude +

etc

You might even be able to do this in Excel and the reverse of this process is called a Fourier Transform, which you won't be able to in Excel!

For the same reason percussive sounds contain a lot of high frequencies, you can only get rapidly changing analog with high frequencies.

That's also while you test high equipment (eps. power amps) with square waves and the resultant should be as square as possible.

That's a bit (pun intended) over-simplified - the samples do pass through the DAC, though they are effectively intentional artefacts (but do not, as you mentioned, represent any additional information or detail beyond that provided by the original bitstream*).

Different (integer-ratio) upsampling algorithms generate different intermediate samples, based on the intended response though the conversion stage.  There are other response characteristics (such as volume decimation or band-specific filtering, e.g., as part of a digital loudspeaker crossover) that can also occur as a part of this process, which also affect the content of the samples.

* - There is some argument to be made for attempting to match the DAC-stage filter response (output) with the original ADC-stage filter response at the point of mastering (input), though it is nearly impossible to know what the ADC-stage response was (or any intermediate D-A-D processes either). Giving the end-user a choice of filter responses may very be a Band-Aid at best....

I know one thing after all this time with Hugo. The "Red-Book" sounds right to me for the first time. I have some old recordings that I liked a lot, but they always sounded poor, edgy and kind of what we call "digital sounding". I went from CD5 to CDX then CDS1, before I stepped into computer playback with DAC-V1. The music I mentioned always had that kind of character, and I was always impressed, it is supposed to sound like it, just bad recordings...wrong!

One of those albums is The Best of The Temptations. Most of that music was recorded back in 60's I guess. I listened to it last night, man, voices, bass, drums, guitars, piano, just name it. Everything sounded just right. I love that album but cymbals especially, always made me tired of listening it, I couldn't stand listening for long time. With Hugo, it is actually opposite, there is so much information in those, and you almost feel you are right there listening them live, drummer is in your living-room.

It was late in the evening, and I was dying to go to sleep, but I just couldn't stop listening...this little machine is amazing.

Bill,

'You have to remember that when our square waves are converted to analog the very process will 'smooth out' the analog produced.   So I have never been sure if interpolation is viable anyway.  I also think that if you do it then you would do the interpolation in the digital domain, difficult to do maths in the analog domain.'

Exactly right, and that is is what the reconstruction IIR or FIR filter is there to do.. That is modify the samples so when they are smoothed into an analogue signal it is done accurately. And this is done usually  by convolvimg or multiplying  the samples with a sinc response using DSP. Now from my sometimes fading memory the accuracy of the  sinc function convolution is dependent on the number of the sinc function samples... And with the Hugo this is unusually high (I believe with the Hugo it is referred to the number of taps based on old analogue delay feedback solutions) due to recent cost effective advancements in low power processing capability. I do wonder if this behind the Hugo's performance.

Simon

I totally agree, i said some pages back that the best thing about Hugo is the fact its opened up all those albums that i just thought were not listenable, because they sounded too congested and, well, like a recording. Well most of them anyway.

It has given these recordings space and some how made them coherent, with instruments that actually sound like an instrument. It is quite uncanny.

It has been 2 months now and still ill play an old album that blows my socks off. It has been without doubt the best value for money upgrade i have made.

Graeme

" It has been without doubt the best value for money upgrade i have made. 

Graeme"

+1

I think Mark said exactly that in his pair of posts!  Mark please correct me if I am wrong.

"the samples do pass through the DAC, though they are effectively intentional artefacts" - are you saying the samples are intentional artefacts?  Not really sure what this sentence means.

Simon, this is exactly what Rob Watts claims, i.e., that an infinite number of taps would permit perfect reconstruction of the signal: a "mathematical certainty", in his words. This seems to be have been one of his key pursuits over the years, with the availability of the Spartan 6 chip providing the computing horsepower to come even closer to this goal. According to the designer, the Hugo's unusually high number of taps accounts for much the naturalness of its sound. So it certainly does not appear to be a "random specification" as been claimed elsewhere in this thread. 

Jan

"intentional artefacts" = deliberate anomalies introduced into digital signals as a result of digital processing, not part of the original signal.  (For that matter, it is entirely possible that there are no original samples that pass through the DAC IC at all.)

...in this case, to enable a better time domain response by shifting the corner frequency of the digital reconstruction filter upward, among other effects....

1) The samples on CD constitute a waveform of tiny steps based on what was originally a smooth analogue waveform. If I drew a smooth line through these tiny steps do you think you could tell this apart from another smooth line fitted to them by someone else?

2) Given you do not have the original analogue waveform as a reference, what would you use as a reference to support the declaration of a new perfect? You cannot use the CD of course so what would you use?

3) How much better is this perfect reconstruction than the best available already and is that worth having even at the expense of other things? For example, if the best now is 99.999% then it can be said perfect is 0.001% better. Is that 0.001% worth having or is it a Pyrrhic victory?

...perhaps the term to use is "least imperfect", i.e., a replay chain that causes the least amount of phase or time distortions during the conversion process from digital bitstream to analogue waveform.

This is, as always, a battle against the law of diminishing returns, though it seems that there is always a surprise around the corner.

Percentages, for that matter, are largely useless for discussions of audio signal quality as we are speaking of improvements at logarithmic scale, rather than linear–therefore small improvements might very well be significant nonetheless.

Least imperfect. I like it.

To help us settle on 'perfect', 'least imperfect' or even plain old 'imperfect', perhaps Jan might advise answers to the three questions?

PS Don't worry about the logarithmic scale, lets just say these are marks out of 100 with 100/100 being equivalent to a perfect analogue reproduction. Least imperfect and varying degrees of imperfect below that. After all, if we cannot say how much better it is, the spectre rises that it is not better at all.

@questions 1 & 2: the analogue waveform is not generated via straight lines; this is a function of the order of the reconstruction filter and, dare I say, could be different depending on whether you play the file forward or reverse, and the type of the filter (FIR vs IIR, among others)!

@question 3: our ears don't work on decimal percentages, and their response varies over the audible range, such that some areas are more sensitive than others.  From this, it follows that spectral plots of clock jitter against a frequency-dependent, equal-loudness contour (rather than a straight logarithmic scale) would show up the differences in performance between DACs more so than the existing measurements.

The Naim DSP algorithm, by the way, uses infinite-impulse response (IIR) filters, while the Chord FPGA implementation uses FIR (finite-impulse response) filters.

Simplified (and potentially grossly incorrect), the FIR filters tend to produce less ringing at the expense of some pre-ringing ("roing", for onomatopoeia's sake), whereas IIR filters will provide a sharp initial impulse with post-ringing thereafter ("boing", hence my remark about the waveform being different, depending on which direction you play the file in!).

IIRs require far less computation to achieve a specified response (lower order), whereas one might have a better shot at a linear phase response with an FIR of much higher order.

The Naim DAC white paper states:

Even though, in a perfect world, FIR should be able to implement any IIR response to the resolution of the DACs, we found that processing loads, arithmetic noise, etc had greater influence on sound quality than the phase errors that IIR filters inherently introduce."

Mark, (cf, your remarks here and in Simon's nDAC and Morrow thread) why don't you ask your questions directly of Rob Watts, as was recommended earlier in this thread, or are you afraid of the answers? You might even learn what a tap is.

Jan

Hi Steve

Is this still planned??

Graeme

Dave, I know you said it was over simplified so I would try and chime in ..   according to Dr Steven W Smiths's superb text, "The Scientist and Engineer's Guide to Digital Signal Processing", which is my DSP bible... the FIR (windowed sinc) and IIR (recursive) filters can be made to perform reasonably similar where moderate performance is required. However for increased performance the FIR starts to leave the IIR behind at the expense of more processing power required.

Until recently this increased performance was difficult for real time processing in consumer devices. An ideal windowed sinc filter has infinite number of samples in the filter kernel otherwise known as the 'ideal filter kernel'. However practically one has to truncate the windowed sinc response by limiting it to a given number of sample points (seemingly referred to as taps in the audio world ). At the point of truncation there is a discontinuity which causes ripple and phase distortion when the nearby samples points are multiplied with the original sample signal. Now as a windowed sinc function decays by a factor of 1/x one gets a disproportionately better response by increasing the number of sinc sample points (taps) in the kernel, and thereby reducing the amplitude of the discontinuity. The Hugo seems to have found by increasing the number of windowed sample points above what is often typically applied, a subjectively better audio response is obtained.. But mathematically the improvements are minuscule and not far above the noise level (in frequency/phase and amplitude), but perhaps we are more sensitive to this in our brains than we thought.. and this is the interesting part to me, and an area that is evolving in understanding. 

Simon

I shall be making a few calls today Graeme to see what the situation is. 

Steve

Steve - the latest issue of HFN has a review of the PS DS DAC. Looks good. 

James

Agreed - it is a fascinating area of study that seems to be fed by an honest appreciation of the notion that we actually know very little about the extreme thresholds of our own hearing, in level, phase, etc., and, more importantly, the way that our brains put this together to appreciate any differences at all that might affect the enjoyment of music (or other audio, for that matter).

Jan, this seems very defensive. In the latest of your very many posts on the Hugo you were reporting claims of perfection. With so many shills on the forum these days, I am sure you will agree it is only reasonable to ask questions when such extravagant claims are posted? Call it consumer protection.

I am not going to search another forum for your answers as I am not the one posting these claims. Give me a free Hugo and perhaps I will be able to muster the interest to take a quick look then report back.

To their credit, Chord's own website does not mention the perfection you highlight. They simply say the Hugo is portable and can play high-res or DSD. A strange choice to omit the whole perfection thing. If it had been me, I would have put it near the top of the page. What would you have done?

Still, their straightforward approach is more appealing than the low-brow viral / advertorial / whatever marketing which we endure so often. A proposterous set of non-sequiturs. Complete vapour. Pseudo-scientific computer babble couched in terms which suggest the opposite is more likely to be true. Often reported second or third-hand. Diluted from easily-dismissible twaddle into complete rubbish. So random and ill-developed yet backed up with such depth of feeling that it risks wearing one down.

DAC's are mature technology. The main differences result from the analogue sections used.

You might get more from pushing for new recording and mastering techniques Wat. As the saying goes, you cannot make a silk purse from a sow's ear.

I agree Wat. However, unencumbered by hi-fi doubt, if I 'just had a listen' at every round of pant-wetting I would spend my entire life just having a listen. Furthermore, the source of encouragement is discouraging.

What I prefer to do is ascertain if there might be substantial reason to have a listen. This thread has led me to realise there is not. I might have had a listen had I never read it. That said, I will listen if and when I decide I want a dedicated portable DAC and one that does DSD. The former need is possible, the latter is currently unforseeable.