I don't know what you call "Nyquist" but it seem to be the filter frequency - which it isn't (it is Fs). When you say brick wall frequency and state a frequency - what drop is that frequency defined as? Surely not - 3dB!?
But yes - the usual spec is to 20k and there everyone likes to state as many zeros as possible (-0,00001 dB etc) and that means a very brutal and steep filter if you want do follow the theorem which say that no signal energy shall be present.
//
Don't let my personal suspicions bias the investigation. Those suspicions may prove to be completely in error. One of the suspect reasons I put on the list has recieved little attention so far. Yet, a quick look at the math surrounding it causes me to raise an eyebrow. For example:
The TDA1541 DAC features a 16-bit settling-time specified at 1uS. I chose it for this example because it makes the math simpler. The DAC's analog output, by definition, is wrong, at a level worse than 16-bits for 1uS, for every sample. So, at a 44.1KHz (NOS) sample rate, a 22.7uS sample period, that settling-time represents a 4.41% error. The sample is in error for 4.41 percent of each sample period.
Increase the rate to 4xOS, and the sample period reduces to one-quarter of the NOS sample period. The DAC's analog output is still is wrong at a level worse than 16-bits for 1uS, every sample. Which means that the percentage of time which the sample is in error at a level worse than a16-bits is now 4 times as much as before. So, 17.64 percent of each sample period.
If this were amplifier distortion, it would represent a level of only -13dB down. While it's not amplifier distortion, neither is it a trivial excercise to ascertain exactly what this sample error means in terms of actual total signal error. For one thing, the settling-time exhibits a non-linear decay, plus it includes glitch energy. However, it does seem a bit surprising at the surface.
It's indeed difficult to say how bad that is. It depends on how much the DAC is off during the settling time and on how close the relation between the error and the signal (or the change of the signal from one step to the next) is to being linear or affine. If the error depends on the change of the signal level from one step to the next, then the oversampling filter doesn't make it (much) worse, because adjacent samples coming out of the oversampling filter will be closer to each other than those that went in.
Two extreme examples:
1. Suppose you had a DAC that produces a perfect staircase waveform followed by a first-order low-pass filter with a time constant of 1 us/ln(65535) ~= 90.169 ns. The settling time of the combination of the two would then be 1 us, but this would not result in any distortion at all.
2. Suppose you had a DAC that produces a perfect staircase waveform followed by an op-amp that goes into slew rate limiting for up to 1 us after each step and then settles instantly. The settling time of the combination of the two would then be 1 us and it would distort like hell.
1. Suppose you had a DAC that produces a perfect staircase waveform followed by a first-order low-pass filter with a time constant of 1 us/ln(65535) ~= 90.169 ns. The settling time of the combination of the two would then be 1 us, but this would not result in any distortion at all.
2. Suppose you had a DAC that produces a perfect staircase waveform followed by an op-amp that goes into slew rate limiting for up to 1 us after each step and then settles instantly. The settling time of the combination of the two would then be 1 us and it would distort like hell.
Could it be improved by using an analog S/H triggered, say 5us after LRCK/WS? Also the sinc drop @20kHz could be reduced by setting the S/H hold period a fraction of the sampling period as I recommended in
shorter hold time
and Jakob2 in
shortening the impulse length
mentioned earlier.
Yes, a properly implemented S/H circuit could be utilized to bypass all of the DAC settling-time issues. As advocated in the attached informative slide presentation created by Frans Sessink way back in 2010.
A S/H circuit can not be utilized to make flat the 20KHz sinc droop, because it inherent provides a hold between samples. This is exactly what zero-order-hold DACs do.
Thanks, very informative. In the meantime I found on Wikipedia:
Zero-order hold - Wikipedia
The last paragraph mentions the Dirac pulses funtion, which would not result in the sinc function HF drop:
The fact that practical digital-to-analog converters (DAC) do not output a sequence of dirac impulses, xs(t) (that, if ideally low-pass filtered, would result in the unique underlying bandlimited signal before sampling), but instead output a sequence of rectangular pulses, xZOH(t) (a piecewise constant function), means that there is an inherent effect of the ZOH on the effective frequency response of the DAC, resulting in a mild roll-off of gain at the higher frequencies (a 3.9224 dB loss at the Nyquist frequency, corresponding to a gain of sinc(1/2) = 2/π). This drop is a consequence of the hold property of a conventional DAC, and is not due to the sample and hold that might precede a conventional analog-to-digital converter (ADC).
A DAC with Dirac pulses output is not practical due to low analog output and poor noise margin after filtering, as mentioned before. But return-to-zero S/H pulses having width a fraction of the sampling period (1/2, 1/3, 1/4?) would approximate such pulses and could still have reasonable energy content.
I found a TI document about it, see attached (pp. 15-16)
Zero-order hold - Wikipedia
The last paragraph mentions the Dirac pulses funtion, which would not result in the sinc function HF drop:
The fact that practical digital-to-analog converters (DAC) do not output a sequence of dirac impulses, xs(t) (that, if ideally low-pass filtered, would result in the unique underlying bandlimited signal before sampling), but instead output a sequence of rectangular pulses, xZOH(t) (a piecewise constant function), means that there is an inherent effect of the ZOH on the effective frequency response of the DAC, resulting in a mild roll-off of gain at the higher frequencies (a 3.9224 dB loss at the Nyquist frequency, corresponding to a gain of sinc(1/2) = 2/π). This drop is a consequence of the hold property of a conventional DAC, and is not due to the sample and hold that might precede a conventional analog-to-digital converter (ADC).
A DAC with Dirac pulses output is not practical due to low analog output and poor noise margin after filtering, as mentioned before. But return-to-zero S/H pulses having width a fraction of the sampling period (1/2, 1/3, 1/4?) would approximate such pulses and could still have reasonable energy content.
I found a TI document about it, see attached (pp. 15-16)
Frans was a colleague of mine until his retirement. If I remember well, he also had a way to check for intermediate rounding errors in digital filters. I don't know the details, but it was something with playing back the same test signal left and right with opposite polarity and a different level, and then making some scaled addition of the output signals.
Yes, the S/H that may precede an ADC chip provides a bit different system purpose than the one that may follow a DAC chip. A post DAC S/H does not shorten the sample’s hold period. It does not help the DAC to approximate Dirac impulse operation by moving it away from a ZOH mode.
As for removing the ZOH based sinc response droop, the better way to address that is by simple analog EQ. This maintains SNR, while also retaining the ZOH sinc envelope that helps to suppress the image bands.
The Decima Digital was one of the many experiments which I performed on my now non-operating AD1865 based NOS DAC over the years. While it is a clever means to obtain RTZ DAC operation, and works as advertised, there are simply better ways to EQ the ZOH based sinc droop, which the Decima approach reduces, but does not fully correct anyhow. From a practical, non-theoretical viewpoint, NRZ (zero-order-hold operation) is superior to RTZ, as far as I'm concerned. Only my opinion.
It always amazes me how many people from such a small country as the Netherlands contribute actively when it concerns digital signal processing.
That has most likely to do with Philips.
I was working in Philips Natlab (physics lab) at the time the CD was conceived, working on a digital radar processing project with many mathematical similarities.
Even after so much time, analog-digital-analog is still a hot topic !
Frans hit the nail on the head whith his statement that it seems ridiculous to criticize the CD with figures far better than Vinyl, but nevertheless, it’s still an open fight.
Hans
That has most likely to do with Philips.
I was working in Philips Natlab (physics lab) at the time the CD was conceived, working on a digital radar processing project with many mathematical similarities.
Even after so much time, analog-digital-analog is still a hot topic !
Frans hit the nail on the head whith his statement that it seems ridiculous to criticize the CD with figures far better than Vinyl, but nevertheless, it’s still an open fight.
Hans
For me it is exactly the oposite: No vinyl has the ability to express the dynamics of a CD if the recordings are from the same master.
16bit (for playback) is more then sufficiant and anything above is just using space on your hard drive and stresses the electronics (cables etc.) because of bandwidth required (unnecessarily so).
I know many people like to show off their huge turn tables and expensive cartidges etc. trying to get the dynamics you could easily get with redbook (can be measured and heard if you have ears). This can be compared with playing with Lego, Trains or scale model boats, it keeps you busy but it's another hobby altogether).
Try this tack (and compare if you can on LP and CD, i can as i have both) No way your LP can deliver the dynamics without distortion (at about 4.30 minutes) !
Gregorio Paniagua - De pastoribus | Mathematica dies irae | Crepuscularis | Sine Nomine (...) - YouTube
16bit (for playback) is more then sufficiant and anything above is just using space on your hard drive and stresses the electronics (cables etc.) because of bandwidth required (unnecessarily so).
I know many people like to show off their huge turn tables and expensive cartidges etc. trying to get the dynamics you could easily get with redbook (can be measured and heard if you have ears). This can be compared with playing with Lego, Trains or scale model boats, it keeps you busy but it's another hobby altogether).
Try this tack (and compare if you can on LP and CD, i can as i have both) No way your LP can deliver the dynamics without distortion (at about 4.30 minutes) !
Gregorio Paniagua - De pastoribus | Mathematica dies irae | Crepuscularis | Sine Nomine (...) - YouTube
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