[sajunky]

Good review, thanks. I always though that the best Chord DAC is a Mojo (the best positioned in the market segment).

 

[lantian]

For anyone interested why r2r is not good solution for audio this article will explain everything.
https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs

 

[ThanatosVI]

For anyone interested why r2r is not good solution for audio this article will explain everything.
https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs

Well it sounds good, so I wouldn't agree on that Statement.

Gonna check the article later

 

[Pondoro]

For anyone interested why r2r is not good solution for audio this article will explain everything.
https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs

This long read is very interesting and well worth the effort, but it only explains why a specific technology took over in the 1989-1990 time period. Along the way it rightly applauds the new technology using cheaper chips and eliminating precision trimming and part sorting. It also displays some bias - the Phillips Corporation is described as large and profitable, and this leads the author to greater optimism about the quality of their DACs. This bias seems to raise the risk that a genius who produces a DAC in his garage would receive unfair reviews. Another bias is revealed by dismissive comments about middle cost CD players. A third display of bias is an obsession with signal measuring precision in the digital world but no compensating caution that mechanical components such as tone arms or bearings or speaker materials also cannot be produced identically. None of this proves anything about what works best in 2021 with today’s chips and the design lessons learned since 1990. Still the article is very interesting in a “Popular Science” manner. But it seems to me that there is an inherent conflict of interest when a reviewer has technological preferences. I’d prefer the reviewer to tell me what a DAC sounds like (and I’ll accept both subjective opinions and measurements.) If the reviewer is a “fan” of a specific technology, or a detractor of another technology, how can I believe I’m getting an unbiased review?

 

[sajunky]

I didn't read the article, but @Pondoro is right on all counts. This fascination of a new technology is still today, as long it is Delta-Sigma technology . The article is very old, little updated over the time. Worth reading, probably yes. But what happened during August last year? We've got two reviews in a row of modern R2R DACs!

Yet, not prepared well... Lets see Holo Audio May review, where John Atkinson dropped a ball in few places. There is a strange pre-ringing in NOS mode:

John Atkinson wrote: "Ignore the very small amount of symmetrical ringing before and after the single full-scale sample, which is due to the antialiasing filter of Audio Precision's A/D converter operating at a sample rate of 200kHz." Possibly, but it doesn't show on other test, it should ring bells. In the next step he tries to explain further: "This graph indicates perfect time-domain behavior due to the absence of a low-pass reconstruction filter". Not true, it is taken on the output which is after a low pass filter. There are two sets of a screenshots from a Russian forum, one is on the DAC output and a second one before a low-pass filter.

The next test shows steps on the 0dBFS sine wave.

A sinewave with 6-bits resolution, really? John Atkinson says: "The DAC's sample-and-hold mechanism results in a "stair-step" waveform." Well, these steps are far, far, far to big - 32 in total or something. Russian srceenshots prompt to think it is something else. Even if true, it would show the same on the Ares II & Terminators test, but it didn't.

Ares II / Terminator test shows some other abnormal behaviour:

This time a conclusion is correct in my opinion, but it should be investigated more. In other words, it should be at least a follow up to the finding, but John Atkinson is not fascinated with the latest R2R technology after all.

It is not that I do condemn Atkinson's work, some others tried to avoid presentation of controversial finding.

 

[dCS James]

James here with a quick update on this series. Thanks to all those of you who've submitted comments so far. We'll be bringing you another post very soon, but we're working on preparing some additional information that we hope will address some of the questions that have come up over the past few weeks.

Thanks for your patience, and we'll be back with a new post on filtering within the next two weeks.

 

[dCS James]

Part 5 – Filtering in Digital Audio​

Most DACs will have some information in their specifications about the types of filtering they use. As these filters are an incredibly important part of the product, it is worthwhile explaining why and how they are used.

To understand why we need a filter, it helps to start at the beginning, when an analogue signal enters an ADC during the recording / production process. (This is significant, as the filter within an ADC has almost as much impact on what we hear during playback as the filter within a DAC.)

We have previously discussed how audio is sampled using an ADC – the analogue voltage is converted into a digital representation, with a series of ‘samples’ being taken to form this representation. The lowest sample rate used in audio is typically 44,100 samples per second (S/s). The reason for using this sample rate (44.1kS/s) is largely due to the Nyquist Theorem. This states that the sample frequency of digital audio needs to be at least twice the highest frequency in the audio being sampled. The highest frequency which can be sampled (half of the sample rate) is defined as the ‘Nyquist frequency’. As the human range of hearing extends up to 20,000Hz, accurately sampling this frequency range requires a sample rate of at least 40,000S/s.

However, what happens if what we are sampling doesn’t ‘fit’ into our sample rate’s valid range, between 0Hz and the Nyquist frequency? If this occurs, then the frequency components above the Nyquist frequency are ‘aliased’ down below it. This sounds counterintuitive, but it is illustrated here:

The above graphs show two signals: one at 1kHz and one at 43.1kHz, both sampled at 44,100 samples per second (44.1kS/s). Note that sampling the 43.1kHz signal produces samples which are indistinguishable from the 1kHz tone (though phase inverted). If this 43.1kHz signal was passed through the ADC, the resultant samples would be indistinguishable from those of the 1kHz tone – and a 1kHz tone would be heard on playback. This means that the ADC must remove anything which does not ‘fit’ between 0Hz and Nyquist frequency, to avoid these aliased images affecting the audio.

The removal of anything which does not fit between 0Hz and Nyquist frequency is carried out by way of a low-pass filter. This filter removes any content above a certain frequency, and allows anything below that frequency to pass through, ideally unchanged. This filter can be implemented in either the digital or analogue realm.

It would seem that the most obvious solution to the aliasing problem caused by running an ADC at a sample rate of 44.1kHz is to implement a filter which does nothing at 20,000Hz, but cuts everything above 20,001Hz. This would allow the removal of any unwanted alias images from the A/D conversion, while ensuring the audio band remains unaffected. However, such a filter is highly inadvisable. For one thing, if using a digital filter, the computing power required to run such a filter would be excessive. Filters work by reducing the amplitude of the signal above a frequency on a slope so to speak, measured in decibels per octave. As such, the audio is sampled at a higher rate than simply double the highest frequency we are trying to record (it is actually sampled at 44,100Hz instead of at 40,000Hz) which allows some room to filter it. This means the filter can now work between 20,000Hz and 22,050Hz without aliasing becoming an issue, while also leaving the audio frequencies humans can hear unaffected.

This diagram illustrates a low-pass filter for 44.1kHz audio.

This is still an extremely narrow ‘transition band’ to play with. If this is done with an analogue filter, the filter will have to be very steep – this is problematic as analogue filters aren’t phase linear (the filter will delay certain frequencies more than others causing audible issues) and are pretty much guaranteed to not be identical. This is okay when they are working at say, 100kHz, but at 20kHz this becomes very problematic. As such, the filter used to remove any content from the Nyquist frequency and up is implemented in the digital domain, in DSP (Digital Signal Processing).

In audio recording, it is common practice to use a high sample rate ADC and perform the filtering at the Nyquist frequency on the digital data instead. This method is known as an ‘Oversampling ADC’. The block diagram for a dCS oversampling ADC producing 16-bit 44.1k data is shown here:

The analogue low-pass filter removes high frequencies from the analogue signal above 100kHz, as these would cause aliasing. As previously discussed, this analogue filter acting at 100kHz can be gentle and acts in a region where non-linearities are not as critical.

The ADC stage then converts the signal to high-speed digital data. In a dCS ADC, this stage is a Ring DAC in a feedback loop, so produces 5-bit data sampled at 2,822,000 samples per second.

The Downsampler converts the digital data to 16-bit 44,100 samples per second. This data then passes through a sharp digital filter, which effectively removes content above 22.05kHz. (Frequencies higher than this will cause aliases if not filtered out.) The PCM encoder then formats the data into standard SPDIF, AES/EBU and SDIF-2 serial formats, complete with status and message information.

The digital filter used in the Downsampler will have its own set of trade-offs to employ. To simplify this greatly, digital filters work by passing each sample through a series of multipliers, with these multipliers collectively acting to filter higher frequencies from the signal. The shape of how these multipliers are arranged is referred to as the filter ‘shape’ (symmetrical or ‘half-band’ filters, asymmetrical filters). Different filter shapes have different impacts on the sound.

This diagram illustrates an example of the response of a symmetrical digital filter. They are called this as they produce symmetrical ‘ringing’ when driven with an impulse (also known as a transient). This results in an acausal response before the impulse. The effect is more pronounced at lower sample rates:

This diagram illustrates an example of an asymmetrical filter response. This filter type has a completely different impulse response – here, there is no ringing before the impulse, but there is more ringing after the impulse when compared to a symmetrical filter:

Given the fact that the ADC must use a filter to remove aliases, and that a digital filter acting at the Nyquist frequency is preferable to using a harsh analogue filter, there will therefore be pre- and/or post-ringing introduced at the recording stage by the digital filtering in the ADC. This is a good trade-off to make, and the filter choice here is important.

Most ADCs will work using a symmetrical filter. What this means is that for any digital recording, there will be (necessary) pre- and post-ringing present on the recording, as a result of the filter which was used. The key point to be made here is that all digital recordings will include ringing from the filters, even before they reach the DAC, but this is the best approach to take – provided the filters are correctly designed and implemented within the ADC.

The other side of this topic is the DAC, where the digital audio recorded by the ADC is translated back to analogue for playback.

When a DAC reproduces an analogue waveform from digital samples, an effect similar to aliasing occurs. This is where, due to the relationship between the frequency of the analogue audio signal and the sample rate of the digital signal, ‘copies’ of the audio spectrum being converted can be observed higher up in the audio spectrum. While these images exist at frequencies outside the range of human hearing, their presence can have a negative impact on sound.

There are two reasons for this. Firstly, frequencies at rates above 20,000Hz can still interact with and have an audible impact on frequencies lower down, in the audible spectrum (between 0-20,000Hz).

Secondly, if these images – known as Nyquist images – are not removed from an audio signal, then the equipment in an audio system may try and reproduce these higher frequencies, which would put additional pressure on that system’s transducers (particularly those responsible for reproducing high frequencies) and amplifiers. Removing Nyquist images means an amplifier has more power available to use for reproducing the parts of an audio signal that we do want to hear, which leads to better performance and a direct positive impact on sound.

Similar to in an ADC, the solution to the problem posed by Nyquist images in D/A conversion is to filter anything above the highest desired frequency of the audio signal by using a low-pass filter. This allows Nyquist images to be eliminated from the audio signal, without impacting the music we want to hear. The question of how a low-pass filter should be designed is a complex and sensitive topic –and it’s important to note that there is no one-size-fits-all solution.

Of course, when working with source material which is at higher sample rates than 44.1kHz, such as hi-res streamed audio, the requirements of the filter in the DAC change. There is a naturally wider transition band, and as such the filter requirements will be different. Most DAC manufacturers offer a single set of filters which are cascaded for different sample rates. Given the different filtering requirements posed by converting different sample rates, this is not the optimal approach to take in a high-end audio system.

For this reason, the filters found within dCS products and the Ring DAC are written specifically for each sample frequency by dCS engineers. Further to this, there are multiple filter choices available for each sample frequency in a dCS product. There is no one right answer to filtering, as it depends on the listener’s preference and the audio being reproduced, so a choice of very high-quality filters bespoke for the Ring DAC and the sample frequency of the audio are available for the user to choose from.

The next post will explore the details of how digital filters are designed for use in audio products, exploring factors such as cut-off frequency, filter length and windowing.

Part 6: Filter Design in ADCs and DACs

 

[sajunky]

This is why those who compared dCS to the MQA fail, as here there is no folding frequencies above Nyquist to the audible band. No a mystery folding/unfolding scam scheme.

On the other side, there is a difference between aliasing during AD conversion and Nyquist images during DA conversion. It is pointed out in the article that aliasing frequencies must be removed, no question about.

A question is whether Nyquist images should be removed is debateable. My answer is, it depends. Filtering images is neccesary when using Delta Sigma conversion method (like dCS does), as in addition to the images, this type of the conversion produce a lot of high frequency noise, the signal-to-noise ratio is only 3dB across all frequencies produced. Filtering this noise also remove images. It is a common misunderstanding that filtering is in purpose of removing Nyquist images, it is neccessary to remove conversion noise.

It comes to another question. Why we should use a method that imply a strict filtering rules with known negative effects (even mentioned in the artticle) or rather use a different conversion method that also produce Nyquist images, but not a correlated HF noise? It is mentioned that Nyquist images can affect negatively our equipment, it is true, but those seeking for an ultimate sound quality would rather invest in better equipment capable of conveying first generation of images without generating distortions. It is a known fact that our ears are not sensitive to the presence of Nyquist images.

 

[Pondoro]

Question: in the block diagram how does the digital filter downstream of the ADC distinguish between a real 1000 Hz signal and a false 1000 Hz signal created as shown in the second picture, created by the 44.1k to 43.1k difference?

 

[rde01]

Question: in the block diagram how does the digital filter downstream of the ADC distinguish between a real 1000 Hz signal and a false 1000 Hz signal created as shown in the second picture, created by the 44.1k to 43.1k difference?

Maybe i should let the pros handle this question because this is hard to explain but i ll give it a try: a ditital filter can not distinguish between frequencies. It affects all digital samples (think of digital filters as series of numeric values that attenuates all samples) and digital samples can contain parts of data of all frequencies. a low pass digital filter can attenuate the high frequency parts of the samples more than the low frequency parts.
If sampled at 44.1k (and without analog filter) the samples of the 43.1k sine would be identical to samples of the 1k sine and a digital filter would have the same effect on them so thats why they sample at higher rates.

I always wondered about this tho: "frequencies at rates above 20,000Hz can still interact with and have an audible impact on frequencies lower down" is that after they have played back and the playback environment had an effect on them?

 

[whitedragem]

Question: in the block diagram how does the digital filter downstream of the ADC distinguish between a real 1000 Hz signal and a false 1000 Hz signal created as shown in the second picture, created by the 44.1k to 43.1k difference?

Based on what I read; is: this ‘effect’ has not yet happened! (?)
-The piece read to me to suggest that that is how that byproduct (freq being misrecorded) based on the low pass aliasing freq beyond Nyquist (a low pass isn’ta ‘low freq’ only affair!) is becoming the output scenario you talk about(the freq, including out of bound freq, artifacts being ‘folded’ together).. at the stage that you are refering, IS the stage that makes it happen, yes(/?); anyone, anyone......

(my presumption is - the first stage GENERATES the aliasing on the out of bound frequencies’ samples/data)

 

[whitedragem]

I always wondered about this tho: "frequencies at rates above 20,000Hz can still interact with and have an audible impact on frequencies lower down" is that after they have played back and the playback environment had an effect on them?

Are we talking here about the science of the recording and the technical nature of recording sound, or, is this to do with the topic of how second harmonics and ‘air’ (around instruments, certainly) affect the appreciable playback of natural sound. That frequencies even ‘outside’ of human hearing range clearly change the appreciable ‘perception’ of the music experience..?

(apols for the double post, but in this instance I figure keeping the topics seperate would allow for any ‘likes’ on the post above to simply allow people to not need to respond in order to concur that the ops’ (orig post, (by Pondoro, not James )) question is null as per belief that the indicated graphic is the active part of the process that ’sees’ the two signals as the op is actually questioning)..

 

[Whitigir]

Question: in the block diagram how does the digital filter downstream of the ADC distinguish between a real 1000 Hz signal and a false 1000 Hz signal created as shown in the second picture, created by the 44.1k to 43.1k difference?

It doesn’t , and that is why different digital filters will have result in a slightly altered performances . But many people claims that all DAC sound the same and all Amp sound the same. IMHO, if you like what you hear, then that is all the matters to this hobby.

 

[IgeNeLL]

Part 5 – Filtering in Digital Audio​

Most DACs will have some information in their specifications about the types of filtering they use. As these filters are an incredibly important part of the product, it is worthwhile explaining why and how they are used.

To understand why we need a filter, it helps to start at the beginning, when an analogue signal enters an ADC during the recording / production process. (This is significant, as the filter within an ADC has almost as much impact on what we hear during playback as the filter within a DAC.)

We have previously discussed how audio is sampled using an ADC – the analogue voltage is converted into a digital representation, with a series of ‘samples’ being taken to form this representation. The lowest sample rate used in audio is typically 44,100 samples per second (S/s). The reason for using this sample rate (44.1kS/s) is largely due to the Nyquist Theorem. This states that the sample frequency of digital audio needs to be at least twice the highest frequency in the audio being sampled. The highest frequency which can be sampled (half of the sample rate) is defined as the ‘Nyquist frequency’. As the human range of hearing extends up to 20,000Hz, accurately sampling this frequency range requires a sample rate of at least 40,000S/s.

However, what happens if what we are sampling doesn’t ‘fit’ into our sample rate’s valid range, between 0Hz and the Nyquist frequency? If this occurs, then the frequency components above the Nyquist frequency are ‘aliased’ down below it. This sounds counterintuitive, but it is illustrated here:




The above graphs show two signals: one at 1kHz and one at 43.1kHz, both sampled at 44,100 samples per second (44.1kS/s). Note that sampling the 43.1kHz signal produces samples which are indistinguishable from the 1kHz tone (though phase inverted). If this 43.1kHz signal was passed through the ADC, the resultant samples would be indistinguishable from those of the 1kHz tone – and a 1kHz tone would be heard on playback. This means that the ADC must remove anything which does not ‘fit’ between 0Hz and Nyquist frequency, to avoid these aliased images affecting the audio.

The removal of anything which does not fit between 0Hz and Nyquist frequency is carried out by way of a low-pass filter. This filter removes any content above a certain frequency, and allows anything below that frequency to pass through, ideally unchanged. This filter can be implemented in either the digital or analogue realm.

It would seem that the most obvious solution to the aliasing problem caused by running an ADC at a sample rate of 44.1kHz is to implement a filter which does nothing at 20,000Hz, but cuts everything above 20,001Hz. This would allow the removal of any unwanted alias images from the A/D conversion, while ensuring the audio band remains unaffected. However, such a filter is highly inadvisable. For one thing, if using a digital filter, the computing power required to run such a filter would be excessive. Filters work by reducing the amplitude of the signal above a frequency on a slope so to speak, measured in decibels per octave. As such, the audio is sampled at a higher rate than simply double the highest frequency we are trying to record (it is actually sampled at 44,100Hz instead of at 40,000Hz) which allows some room to filter it. This means the filter can now work between 20,000Hz and 22,050Hz without aliasing becoming an issue, while also leaving the audio frequencies humans can hear unaffected.


This diagram illustrates a low-pass filter for 44.1kHz audio.

This is still an extremely narrow ‘transition band’ to play with. If this is done with an analogue filter, the filter will have to be very steep – this is problematic as analogue filters aren’t phase linear (the filter will delay certain frequencies more than others causing audible issues) and are pretty much guaranteed to not be identical. This is okay when they are working at say, 100kHz, but at 20kHz this becomes very problematic. As such, the filter used to remove any content from the Nyquist frequency and up is implemented in the digital domain, in DSP (Digital Signal Processing).

In audio recording, it is common practice to use a high sample rate ADC and perform the filtering at the Nyquist frequency on the digital data instead. This method is known as an ‘Oversampling ADC’. The block diagram for a dCS oversampling ADC producing 16-bit 44.1k data is shown here:



The analogue low-pass filter removes high frequencies from the analogue signal above 100kHz, as these would cause aliasing. As previously discussed, this analogue filter acting at 100kHz can be gentle and acts in a region where non-linearities are not as critical.

The ADC stage then converts the signal to high-speed digital data. In a dCS ADC, this stage is a Ring DAC in a feedback loop, so produces 5-bit data sampled at 2,822,000 samples per second.

The Downsampler converts the digital data to 16-bit 44,100 samples per second. This data then passes through a sharp digital filter, which effectively removes content above 22.05kHz. (Frequencies higher than this will cause aliases if not filtered out.) The PCM encoder then formats the data into standard SPDIF, AES/EBU and SDIF-2 serial formats, complete with status and message information.

The digital filter used in the Downsampler will have its own set of trade-offs to employ. To simplify this greatly, digital filters work by passing each sample through a series of multipliers, with these multipliers collectively acting to filter higher frequencies from the signal. The shape of how these multipliers are arranged is referred to as the filter ‘shape’ (symmetrical or ‘half-band’ filters, asymmetrical filters). Different filter shapes have different impacts on the sound.

This diagram illustrates an example of the response of a symmetrical digital filter. They are called this as they produce symmetrical ‘ringing’ when driven with an impulse (also known as a transient). This results in an acausal response before the impulse. The effect is more pronounced at lower sample rates:



This diagram illustrates an example of an asymmetrical filter response. This filter type has a completely different impulse response – here, there is no ringing before the impulse, but there is more ringing after the impulse when compared to a symmetrical filter:



Given the fact that the ADC must use a filter to remove aliases, and that a digital filter acting at the Nyquist frequency is preferable to using a harsh analogue filter, there will therefore be pre- and/or post-ringing introduced at the recording stage by the digital filtering in the ADC. This is a good trade-off to make, and the filter choice here is important.

Most ADCs will work using a symmetrical filter. What this means is that for any digital recording, there will be (necessary) pre- and post-ringing present on the recording, as a result of the filter which was used. The key point to be made here is that all digital recordings will include ringing from the filters, even before they reach the DAC, but this is the best approach to take – provided the filters are correctly designed and implemented within the ADC.

The other side of this topic is the DAC, where the digital audio recorded by the ADC is translated back to analogue for playback.

When a DAC reproduces an analogue waveform from digital samples, an effect similar to aliasing occurs. This is where, due to the relationship between the frequency of the analogue audio signal and the sample rate of the digital signal, ‘copies’ of the audio spectrum being converted can be observed higher up in the audio spectrum. While these images exist at frequencies outside the range of human hearing, their presence can have a negative impact on sound.

There are two reasons for this. Firstly, frequencies at rates above 20,000Hz can still interact with and have an audible impact on frequencies lower down, in the audible spectrum (between 0-20,000Hz).

Secondly, if these images – known as Nyquist images – are not removed from an audio signal, then the equipment in an audio system may try and reproduce these higher frequencies, which would put additional pressure on that system’s transducers (particularly those responsible for reproducing high frequencies) and amplifiers. Removing Nyquist images means an amplifier has more power available to use for reproducing the parts of an audio signal that we do want to hear, which leads to better performance and a direct positive impact on sound.

Similar to in an ADC, the solution to the problem posed by Nyquist images in D/A conversion is to filter anything above the highest desired frequency of the audio signal by using a low-pass filter. This allows Nyquist images to be eliminated from the audio signal, without impacting the music we want to hear. The question of how a low-pass filter should be designed is a complex and sensitive topic –and it’s important to note that there is no one-size-fits-all solution.

Of course, when working with source material which is at higher sample rates than 44.1kHz, such as hi-res streamed audio, the requirements of the filter in the DAC change. There is a naturally wider transition band, and as such the filter requirements will be different. Most DAC manufacturers offer a single set of filters which are cascaded for different sample rates. Given the different filtering requirements posed by converting different sample rates, this is not the optimal approach to take in a high-end audio system.

For this reason, the filters found within dCS products and the Ring DAC are written specifically for each sample frequency by dCS engineers. Further to this, there are multiple filter choices available for each sample frequency in a dCS product. There is no one right answer to filtering, as it depends on the listener’s preference and the audio being reproduced, so a choice of very high-quality filters bespoke for the Ring DAC and the sample frequency of the audio are available for the user to choose from.

The next post will explore the details of how digital filters are designed for use in audio products, exploring factors such as cut-off frequency, filter length and windowing.

Thanks this topic is really useful and concise, looking forward to the next topic.
Anyway, does DCS have testing between the symmetrically shape of filter and effect of its to the user ( kind of sound signature of filter)

 

[SilverEars]

But does it cost reasonably and sound good? lol