Really? Damn did not know that and I missed it.
They wonāt because they are band limited. There is little point reproducing frequencies beyond the limits of human hearing. Your argument is moving towards pedantry: such details are not relevant to the OP.
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That band limiting causes various side-effects as I mentioned. Thereās no āperfect band limitingā.
You cannot tell a violin, or a drum kit to stop producing frequencies above 22.05 kHz. They will do that whether you like it or not.
But the reconstruction can attempt to take those side-effects / imperfections into account in the reconstruction process, and attempt to correct at least the worst errors.
To properly reconstruct 24-bit 44.1 kHz sampled signal. You must reject anything beyond 22.05 kHz by 144 dB or more. So you can see how deep low-pass filter you will need for that. And there are many ways doing such low-pass filter. Some have for example better transient response, some worse.
As you should know, 44.1k sampled signal will repeat itās spectrum as inverse form 22.05 to 44.1 kHz. And then again forward replica from 44.1 to 66.15 kHz and then again reverse frequencies from 66.15 to 88.2 kHz, and so on. (and also mathematically, similar negative frequencies)
You can choose to reproduce those, or deal with the side-effects of the band-limiting. In particular the time domain side-effects of the band limiting.
If you record and playback in DSD, you donāt need band limiting. As the Nyquist frequency (half the sampling rate) is way up in the MHz range.
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Our ears are band-limiting and dynamically compressing the input sound pressure waves. Thus, we only need to faithfully reproduce what can be heard in the first place, otherwise it woud be a useless effort.
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Yeah, that doesnāt remove the fact that the band limiting at ADC side causes side-effects.
But returning to the original topic, you know, thereās a reason why all modern D/A converters are oversampled delta-sigma typeā¦ PCM to DSD conversion is this same process, just replacing the on-chip process with external one.
But of course not all delta-sigma modulators are one bit, so they donāt all produce DSD. Many - if not the majority of - on-chip modulators produce 4-6 bits, which allows for proper dithering and de-correlating of the quantization noise (e.g. through TPDF), something DSD cannot do.
For example ESS Sabre produces 1-bit stream. And it can indeed be properly dithered and decorrelated. For example HQPlayerās ASDM7EC-ul/light/fast/super modulators are fully dithered, all errors are way below -300 dB. And thereās also AHM7EC8B 8-bit modulator for producing 1-bit stream, which is also fully dithered.
If you donāt know how to do it, it doesnāt mean it cannot be done. It was mathematically proven about ten years ago that 1-bit modulator can indeed be fully dithered. The mathematical proof for that is certainly not simple.
I have also shown using measurements, that audio band performance of ES9039 can be improved by running it with DSD512 data, compared to 32-bit 44.1k PCM input. Same applies for various AKM chips as well, switched to DSD Direct mode where the data passes straight to the D/A conversion stage.
I have proven mathematically that itās impossible to do that with one bit, so I wonāt continue down this path. (And that proof is quite simple.)
Yes, you can bring errors below audibility, but theyāre still correlated. We need to be technically accurate.
No they are notā¦
You need to practice your math a bit moreā¦ 
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Yes they are. This is the high end of the spectrum of a 1kHz sine modulated to DSD. You can clearly see the 1kHz-spaced peaks (even and odd), indicating signal correlation:
This is the same sine modulated to 4 bits (15 levels) with TPDF. Not only is the overall noise level some 20dB lower, the spectrum is completely random:
Modulated using what modulator? It is completely useless to discuss this without talking about the exact modulator.
I addition, top end of the spectrum, or even half of the spectrum is not going through the D/A conversion. It gets already removed by the multi-element conversion stage (analog FIR) and also by the analog reconstruction post-filter.
Here is top end of the spectrum with AHM7EC8B, 1k tone:
If we then compare the output to what comes out for example from typical AKM based DAC analog outputs, with 0 - 22.05 kHz sweep from 44.1 kHz source data:
We can see that the on-chip 8x digital filter is not even nearly sufficient and produces massive amount of fully correlated images throughout the ultrasonic spectrumā¦
While if we look at similar spectral range, without any reconstruction filters involved with pure DSD data:
It is completely clean.
ASDM7ECv3. Please let me know which modulator you think can produce a 100% decoupled DSD quantization noise and Iāll take a look.
Thatās irrelevant for my point: DSD quantization noise will never be fully decorrelated - regardless of whether that is audible in the 20Hz-20kHz band or whether itās going to be filtered out etc. Thereās no need to show me analog output spectra, and thereās no need to look into what DAC chips do. I would appreciate it if you stopped deflecting for once.
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Some old/unofficial software?
Try the above mentioned AHM7EC8B for example.
That is the most important thing, since that is what we are listening toā¦ So of course we need to do precisely that. We are listening to analog output from the DACs, so that is my main focus on developing all the algorithms. That means a lot of measurements from wide variety of different DACs. And of course also ADCs.
Sole purpose of the whole thing is the produce accurate analog audio output!
For example RME ADI-2 Pro, 44.1k input:
High level of fully correlated images.
RME ADI-2 Pro, DSD256 input:
Just uncorrelated noise, about 40 dB lower level, and nothing beyond 800 kHz.
HQPlayer 5.16.1.
But that doesnāt make it ok to say that the algorithms do something they canāt, namely that they can completely decorrelate DSD quantization noise. If you stop saying that, Iāll stop nagging. Also, this has nothing to do with HQPlayer itself, itās inherent to DSD.
I canāt make that work. Iāll follow up offline.
Yes they can, that is what I have shown above. And AHM7EC8B is my latest creation.
While if we look at āmultibitā SDM DACs like Chord claims to beā¦
From a Chord DAC, with sweep we get this kind of output:
And then we switch to 1 kHz tone we get this:
You can see itās modulator produces a lot of correlated ultrasonic noise modulation. Many DAC chip modulators also produce both spurious tones and ultrasonic noise modulation. While my modulators donātā¦
Followed up with Jussi. AHM7EC8B only works with DSD1028, so I canāt use it. Is there another modulator that supports DSD512 and can pull that off?
I changed my ASIO grabber and now it supports everything you throw at it, so I was able to use AHM7EC8B modulator with DSD1028. I converted two signals separately, a 1kHz sine and a 5kHz sine, and plotted both spectra together. This is the full range (log):
There are two really big idle tones, one at 128fs (which goes up to 0dB!) and another at 384fs. (I guess they were symmetrical around the 256fs center, but the high end of the spectrum looks attenuated.) The ātoneā visible at 256fs is actually two tones close together - at 256fs-1000kHz and 256fs+1000kHz for the 1kHz sine, and at 256fs-5000kHz and 256fs+5000kHz for the 5kHz sine - rising almost 30dB above the random noise:
So, not only is the noise not entirely random, itās still correlated with the signal.
Trying to decorrelate DSD noise is like trying to solve the 14-15 puzzle.
No it is not correlated (within the Nyquist bandwidth of 5.6 MHz).
And they are not idle tones either. They are images, which you will also get always with PCM data, at multiples of the sampling rate. So if you use a multibit modulator, the spectrum will repeat itself at multiples of the sampling rate. Remember that this is not Nyquist sampled data.
This is what you get also with the multi-bit DAC chips as I have shown before. This is fundamental difference between 1-bit and multibit converters. Multibit converters will always have spectral images of the input signal at multiples of their input rate. And spectral images are always correlated. This happens when word length is not entirely filled with pure noise. More bits you have (longer the word length), stronger the images will be compared to the noise level.
It is entirely random as you can see from your own plot. You just donāt seem to understand what you are looking at.
Up until first image, the two spectras perfectly overlay with no difference. And also beyond that, the noise floor is completely identical.
Remember that the full band output data amplitude is always the same, 0 dB! Donāt be fooled by FFT, because the 0 dB noise is spread over wider spectrum than discrete tones.
Yes, as images are.
So whenever you use a multibit converter, you will always have images in the digital output data, at multiples of the sampling rate. Also in your own example when you expand the spectrum for example to cover 8 times the sampling rate. Remember that the spectrum doesnāt end at fs/2, but it continues ad infinitum.
And images are of course always correlated as I have shown in above measurements. And DAC reconstruction filter needs to remove these ultrasonic things, be it DSD noise or PCM images.
Apart from the images you will always have with multi-bit data, you can clearly see the noise floor is totally uncorrelated.
So DSD always gives lowest possible level of correlated ultrasonic tones/images on unlimited bandwidth, because it has lowest peak-to-noise ratio!