advertisement


chord 1,000,000 taps

Yes. A brick wall filter is theoretically optimal. It is also not technically difficult to implement, and early CD players did employ them to comply with what we understand mathematically about sampling theory.

However, as the measurement of what was being done within the pass-band became more sensitive, manufacturers and testers began to realise that the pass-band effects of genuine brick wall filters were harmful. The 'sharper' the filter the more of a 'ripple' effect it can cause in the pass band.

Many manufacturers deploy a wide range of techniques to try and emulate the theoretical benefits of a brick wall without causing undue harm in the pass band. Chord's technique is one of many. Other manufacturers, who produce equipment that is both technically and subjectively very accomplished, apply very different techniques and often use much gentler filters.

I own both a Chord Mojo and a Chord Hugo and I find both to be very impressive pieces of kit. I have also heard the Hugo 2 and the Mojo 2 which are excellent.

The criticism that emerges of them, from those who do not enjoy them, is that they are highly analytical sounding. I think that is a very fair criticism but, as it happens, I like to analyse the music I am listening to. I also find the Hugo in particular to be very viscerally involving.

Chord produce some outstanding kit and is a good British success story.
Thanks for your explanations. When you say ripple effect, do you mean like an echo, i.e. a replication of the signal after a certain time delay? if this is so, I presume using more taps means less ripples?
 
Thanks for your explanations. When you say ripple effect, do you mean like an echo, i.e. a replication of the signal after a certain time delay? if this is so, I presume using more taps means less ripples?

I'm not sure you're thinking about it right.

The original attempts which caused problems were analog domain implementations of a brickwall filter to remove aliases.

Instead of doing this, we these days resample the audio from 44.1Khz to some higher multiple of this, let's say 8x oversampled, to 352.8Khz. Every 8th sample value is the original supplied value, then the next 7 are interpolated from the original sample values. The algorithm used to create these extra 7 samples is the above mentioned sinc interpolation algorithm, as this defines the actual values which appear 'between' the sample values, and hence the DAC filter calculates these values.

The resulting signal will have the original 22.05Khz bandwidth, with no signal up to the new nyquist frequency of 176.4Khz. Building a higher speed digital to analog converter knowing that there is no signal above 22.05Khz, and the next frequencies that will be seen are above 300KHz is much easier to make.

The thing chord is doing is building a very large FIR filter with a large number of taps to implement the sinc filter used for interpolation, rather than a shorter windowed sinc. Inaccuracies in the filter will not introduce any sort of ripple, it will introduce comb filtering maybe, but at such a low level as to be not recognisable as such. Really, the difference between the longer and 'traditional' sinc filters will be maybe a least significant bit difference every now and again. The large FIR filter will introduce some additional latency since it needs to look into the future, and this is achieved by having a buffer of previously received sample data in order to apply the filter coefficients. This is true for all FIR filters, there is always some delay. Commercial DACs for pro audio (my field) typically introduce 32 samples of delay, so around 1ms. The chord will be much longer than this, but for music reproduction it makes no meaningful difference.
 
Does it matter? Is this too many taps for the reconstruction filter? I'll leave that to other people with better ears to argue about, but the engineering is sound which makes a change from lots of the other weird foo we generally have to deal with.
Good engineering is about having a balance, enough but not wasteful. There is a point where going too far becomes bling
 
Good engineering is about having a balance, enough but not wasteful. There is a point where going too far becomes bling
That does sound sensible but who is to decide when, as you put it, balance becomes bling. Are you saying that Chord’s m scaler is bling? If so how did you arrive at this conclusion? How long did you assess an m scaler and or Chord DAC for and in what sort of system?
 
I'm not sure you're thinking about it right.

The original attempts which caused problems were analog domain implementations of a brickwall filter to remove aliases.

Instead of doing this, we these days resample the audio from 44.1Khz to some higher multiple of this, let's say 8x oversampled, to 352.8Khz. Every 8th sample value is the original supplied value, then the next 7 are interpolated from the original sample values. The algorithm used to create these extra 7 samples is the above mentioned sinc interpolation algorithm, as this defines the actual values which appear 'between' the sample values, and hence the DAC filter calculates these values.

The resulting signal will have the original 22.05Khz bandwidth, with no signal up to the new nyquist frequency of 176.4Khz. Building a higher speed digital to analog converter knowing that there is no signal above 22.05Khz, and the next frequencies that will be seen are above 300KHz is much easier to make.

The thing chord is doing is building a very large FIR filter with a large number of taps to implement the sinc filter used for interpolation, rather than a shorter windowed sinc. Inaccuracies in the filter will not introduce any sort of ripple, it will introduce comb filtering maybe, but at such a low level as to be not recognisable as such. Really, the difference between the longer and 'traditional' sinc filters will be maybe a least significant bit difference every now and again. The large FIR filter will introduce some additional latency since it needs to look into the future, and this is achieved by having a buffer of previously received sample data in order to apply the filter coefficients. This is true for all FIR filters, there is always some delay. Commercial DACs for pro audio (my field) typically introduce 32 samples of delay, so around 1ms. The chord will be much longer than this, but for music reproduction it makes no meaningful difference.
Thank you for your reply. I remember from reading the brochures of the Wadia dacs that an impulse signal is impossible to replicate because it has infinite frequencies. Digital filtering will end up creating an approximation with ringing or "ripples" from either side of the signal. I thought that's what the gentleman referred to and by increasing the number of taps, Chord will reduce the ripples.
 
When an original signal has high frequency content, in particular frequencies approaching 22kHz, and then it's band-limited for 44.1kHz then you get the ripples. This band-limiting is absolutely necessary for a correct set of 44.1kHz samples to be acquired. Note at this point, a DAC hasn't even made it into the picture!

Hence all the talk of impulse response of a DAC is nothing to do with artifacts added by the DAC. (In reality it's more about how the DAC will deal with any artifacts that may be already baked into its input.)

A perfect DAC will reproduce such pre-existing 44.1kHz ripples, if they are present, perfectly. Other DACs that are technically unconventional may do other things with the ripples.

That's why I wrote that reproducing the original analogue accurately, and reproducing a 44.1kHz signal accurately, are arguably not the same thing.
 
Thank you for your reply. I remember from reading the brochures of the Wadia dacs that an impulse signal is impossible to replicate because it has infinite frequencies. Digital filtering will end up creating an approximation with ringing or "ripples" from either side of the signal. I thought that's what the gentleman referred to and by increasing the number of taps, Chord will reduce the ripples.

Well, yes and no. An impulse is really defined within the digital domain to mean a signal with 0 for all time except at one moment where the value is non-zero. This signal has the property that it contains an equal amount of all frequencies up to the Nyquist frequency (which is defined by 1/2 the sample rate). So the digital signal has a very well defined meaning, and does not have infinite bandwidth. The above mention of the sinc function is actually the correct continuous domain representation of how the voltage should change to represent such a signal when passed through a DAC. It's actually so fundamental that it's really the *only* measurement that you need to obtain from a DAC to see how it performs (weird isn't it?).

Here's an impulse in the digital domain with the expected output overlayed:

RBz9lM4.png


The dots represent the samples, the blue line is the expected output voltage from the DAC which would be generated for such an input. The curve passes through all the zero sample before and after the non-zero sample, but wobbles above and below the zero line.

Now you've probably heard of different reconstruction filters, and there are choices other than sinc, they are basically the same function but with the phase non-linear, with the 'benefit' of changing the amount of pre-ringing.

For example, the above impulse sent out the headphone socket on my macbook and captured on an oscilloscope looks like:

9uFaEeV.png


Which is definitely not the sinc function we see above! However, we can see much more ringing after the impulse, it's almost as if the energy has to come out somewhere isn't it? ;)

If we zoom in on this tail and stick some cursors on, we can see the sample rate showing this is basically doing the same frequency 'wobble' as above:

rlRnrPy.png


You can tell from this that my sample rate is 44.1Khz, measurement imprecision withstanding.

Does this kind of help or am I just causing more confusion?

Take away - an impulse gives some sort of nyquist frequency ringing in the output, which can be pre or post the event. It's not a bug, it's correct (well, the above is not correct, that's a modified response in order to make the implementation easier, probably some sort of IIR filter but we're getting far off point to cover that sort of thing).

If I were to overlay the frequency response of the impulse, it would be essentially flat out to Nyquist. The difference in the above plot vs the pre-ringing one would be visible in a phase shift across the frequencies, not the amplitudes. So, if you think that phase should be preserved at all costs, you want a DAC with pre-ringing. If you think that pre-ringing is the work of the devil, you end up with phase inaccuracies. Trading one off against the other to produce a pretty picture is left as an exercise for the reader.

P.S I can't hear the difference between different filter types, and if pre-ringing was so terrible it would be obvious right? It's not clear what the chord filter response is, it could be either of these, or something in between. The fact they talk in their marketing about some special filter would suggest it's not straight sinc, but it won't be far off.
 
Well, yes and no. An impulse is really defined within the digital domain to mean a signal with 0 for all time except at one moment where the value is non-zero. This signal has the property that it contains an equal amount of all frequencies up to the Nyquist frequency (which is defined by 1/2 the sample rate). So the digital signal has a very well defined meaning, and does not have infinite bandwidth. The above mention of the sinc function is actually the correct continuous domain representation of how the voltage should change to represent such a signal when passed through a DAC. It's actually so fundamental that it's really the *only* measurement that you need to obtain from a DAC to see how it performs (weird isn't it?).

Here's an impulse in the digital domain with the expected output overlayed:

RBz9lM4.png


The dots represent the samples, the blue line is the expected output voltage from the DAC which would be generated for such an input. The curve passes through all the zero sample before and after the non-zero sample, but wobbles above and below the zero line.

Now you've probably heard of different reconstruction filters, and there are choices other than sinc, they are basically the same function but with the phase non-linear, with the 'benefit' of changing the amount of pre-ringing.

For example, the above impulse sent out the headphone socket on my macbook and captured on an oscilloscope looks like:

9uFaEeV.png


Which is definitely not the sinc function we see above! However, we can see much more ringing after the impulse, it's almost as if the energy has to come out somewhere isn't it? ;)

If we zoom in on this tail and stick some cursors on, we can see the sample rate showing this is basically doing the same frequency 'wobble' as above:

rlRnrPy.png


You can tell from this that my sample rate is 44.1Khz, measurement imprecision withstanding.

Does this kind of help or am I just causing more confusion?

Take away - an impulse gives some sort of nyquist frequency ringing in the output, which can be pre or post the event. It's not a bug, it's correct (well, the above is not correct, that's a modified response in order to make the implementation easier, probably some sort of IIR filter but we're getting far off point to cover that sort of thing).

If I were to overlay the frequency response of the impulse, it would be essentially flat out to Nyquist. The difference in the above plot vs the pre-ringing one would be visible in a phase shift across the frequencies, not the amplitudes. So, if you think that phase should be preserved at all costs, you want a DAC with pre-ringing. If you think that pre-ringing is the work of the devil, you end up with phase inaccuracies. Trading one off against the other to produce a pretty picture is left as an exercise for the reader.

P.S I can't hear the difference between different filter types, and if pre-ringing was so terrible it would be obvious right? It's not clear what the chord filter response is, it could be either of these, or something in between. The fact they talk in their marketing about some special filter would suggest it's not straight sinc, but it won't be far off.

First of all, thank you so much for all of this work. I am not sure I understand it all but the impulse function i am referring to is a short and sharp frequency impulse. If the sine wave in your first diagram is the result output of this function then clearly it is not a very good copy! Secondly, if the yellow graph is a reconstructed copy of the first sine wave then it is rather disappointing. I seem to remember wadia managed to create a much closer copy using their proprietary algorithm. I'll be interested to see the same results from a Chord DAC. Sorry if I misinterpreted your results. Entirely my fault.
 
First of all, thank you so much for all of this work. I am not sure I understand it all but the impulse function i am referring to is a short and sharp frequency impulse. If the sine wave in your first diagram is the result output of this function then clearly it is not a very good copy! Secondly, if the yellow graph is a reconstructed copy of the first sine wave then it is rather disappointing. I seem to remember wadia managed to create a much closer copy using their proprietary algorithm. I'll be interested to see the same results from a Chord DAC. Sorry if I misinterpreted your results. Entirely my fault.

Yes, we're talking about the same test signal, an impulse. As for the first picture, this is the hard bit to get your head around, but that blue curve is *exactly* what you describe, it is a mathematically perfect impulse bandlimited to nyquist. The fact that your brain says 'that looks horrible, and can't possibly sound like a click' is why this stuff is hard, is basically because the time interval we're dealing with it so very small. DAC manufacturers have tried very hard to recreate exactly that shape, and are very good at it. Your DAC basically does this for every sample played back, so 44.1 thousand times per second, and sums those curves together to form the output signal you get.
 
Cesare's posts include discussion of how impulse response figures in the implementation of a DAC's reconstruction filter. My posts are mostly not about DACs. Two examples:

(1) original analogue signal with NO frequencies in 20-22kHz range:

analogue -> 44.1kHz no ringing/ripples -> DAC uses funky ripply impulse response sums across a window -> outputs analogue with no ringing/ripples.

(2) original analogue signal with frequencies in 20-22kHz range:

analogue -> 44.1kHz with ringing/ripples -> DAC uses funky ripply impulse response sums across a window -> outputs analogue with only "original 44.1kHz" ringing/ripples.

--

So there is no contradiction here, the posts are all consistent because they're about different aspects.
 
Last edited:
That does sound sensible but who is to decide when, as you put it, balance becomes bling. Are you saying that Chord’s m scaler is bling? If so how did you arrive at this conclusion? How long did you assess an m scaler and or Chord DAC for and in what sort of system?
Mscaler may do what it is meant to do but it is unlikely to provide any audible benefits. The manufacturer has failed to demonstrate them.
 
Yes, we're talking about the same test signal, an impulse. As for the first picture, this is the hard bit to get your head around, but that blue curve is *exactly* what you describe, it is a mathematically perfect impulse bandlimited to nyquist. The fact that your brain says 'that looks horrible, and can't possibly sound like a click' is why this stuff is hard, is basically because the time interval we're dealing with it so very small. DAC manufacturers have tried very hard to recreate exactly that shape, and are very good at it. Your DAC basically does this for every sample played back, so 44.1 thousand times per second, and sums those curves together to form the output signal you get.
Thank you again for your time.
 
Bl00dy hell @Cesare I think that the explanations above are about the best I've seen. Starting to understand this a little better. :)
So am I right in thinking that if you had infinite bandwidth, you'd produce a perfect square wave of one period (at your 44.1k) long? Band-limiting means that you have effectively stripped away all the harmonics that you need to make the perfect impulse (as these are above the Nyquist frequency.)
 


advertisement


Back
Top