You’re clutching at straws. Calculation ≠ measurement. But measurements tell us how close we are to calculated values. We can measure to a very high degree of precision for all things relating to hi-fi sound systems.
As I’ve already stated elsewhere in this thread, the science doesn’t support this point of view. The research is freely available if you care to take a look.
And what calculated values are measurement compared with today? Typically nothing or a 12khz tone. What I am saying is that is clearly not enough, or we would not have DACs that measures well and sound horrible (like the Topping DX34 DAC which I have used as an example since I own that DAC myself).
Its possible to calculate a perfect reconstruction similar to what Nyquist talked about in the beginning of the 80, as long as you have 2 samples or more/frequencies. However, its very computational expensive and it also requires the whole signal, which means a DAC can’t do it. But software can do it.
And this will truly be a perfect signal, 100% lossless, and differences from this will be steps away from transparency. This is how measurements should be done (I know its not how its done today).
Just to clarify, you can do a lot of measurements for a lot of situations, but what I am describing is a possible way to make a measurement that tells more about how something sounds than the current measurements.
For example, the reconstruction filter in a typical DAC is an approximation, but how good approximation is it? You certainly won’t know that from a 12khz test tone. So why not compare it to a perfect signal calculated in advance?
Eh?
What are you talking about? Are you suggesting that Fourier transforms are an appoximation of the original waveform? That’s not what I learned in my acoustics course. Admittedly that was some 35 years ago, but still…
Now I’m going to appeal to members with an engineering/electronics background to corrrect me if I’m wrong. I am under the impression that a low pass filter in a DAC is an analog filter, so there are no calculations, just limitations on the frequencies that are passed along.
And even if a digital filter would be used, then the calculation will not output an approximation but will reconstuct the original waveform by performing an inverse Fourier transform. It’s a long long time ago that I swotted this stuff, but I seem to remember this quite clearly.
What Nyquist said was that as long as you have 2 samples or more / frequency, you can accurately calculate the sine wave that passes through those samples. However, since a sine wave never reach 0 every point along the signal will be a sum of all sine waves, hence you need the whole signal.
Granted, the approximations that can be done in DACs are fairly accurate in theory. But then there is also accuracy issues, crystal inaccuracies, analog stage and so on. From a transparency viewpoint, the DAC should get as close as possible to the perfect signal that is defined with the samples.
However, as far as I know, there are no measurements that even tries to measure this. Instead we have jitter measurements, crossover measurements, SNR measurements and so on. All valid, but just a small subset of what would be needed to fully measure transparency.
And how would you output the result of that calculation? As an analogue waveform, perhaps?
So you have a “device” that takes a digital signal as input, and produces an analogue waveform as output. And it does so “perfectly”. All you need is a stylish anodized aluminum case for your device, and you can sell The Magnus for $$$$.
(One might object that The Magnus doesn’t have to do its computation in real-time (unlike a conventional DAC). But then you have to store your analogue waveform for later comparison. How would you like to do that storage? Perhaps as bumps on a vinyl disk?)
Yes, at least it is my design. Although I can machine and weld steel, I was at the end of my art here. This is stainless steel, I need tools that I don’t have to machine it. To bend these radii you need e.g. a press with a pressure of 100 tons. Fortunately, I have a tinsmith in the neighborhood who masters this profession. The slabs on it are black granite, which I had cut to size. They are not firmly connected, they rest on 5mm thick felt strips.
Very nicely done.
Absolutely beautiful 
THAT is worth paying a premium for. Beautiful design and work!
What’s the nut for?
You don’t need to store the analogue wave, instead you store math information so its easy to reconstruct. In this case, perhaps a set of points/amplitude/frequency for each sine wave (although the whole sine wave is not used, only one peak or dip). Everything stored as 64 bit double, and then calculated when needed.
Or you just calculate from the original 44/16 data on the fly, and don’t store anything. Unlike digital audio, we don’t need to do that calculation in real time when playing music, but can instead be processed in any time-frame.
Here is an example with signal cables:
You have just described PCM digital audio (using 64 bit float, rather than 24 bit integer, but the conversion between those two is, for all practical purposes, lossless as the “rounding error” is way below the threshold of audibility).
What do you mean “unlike digital audio” What you are describing (minus all of the technical details which would make it correct) is digital audio.
Digital audio is nothing more nor less than a way of encoding an analogue waveform as a sequence of numbers, from which you can reconstruct the original analogue waveform later.
I realize you are trying to reinvent the whole science of digital audio on the fly, but you might want to think a bit and do some internet research before posting more.
A lot of smart people have spent decades thinking about how best to do that. I kinda doubt that you are going to come up with a better solution on the fly.
Yes, but the reconstruction filter in a DAC is not 100% accurate, its an approximation. And there are also several other parts that will affect the final output (clocks, jitter, analog stage, electronic noise and so on). If every DAC perfectly recreated the original analog signal, then every DAC would sound the same.
But by comparing the actual output of an DAC to a perfect signal, you can calculate deviance and deduce lots of information, but the input has to be real music and not just some simplified 12khz signal.
As I said above, if you have a device which can take the original digital data and reconstructs the “perfect signal” from it, then what you have is a DAC.
If The Magnus is a better DAC than all of the others currently on the market, then you will soon be a very rich man.
You can cut to the chase and get to the technical summary at 28:15. 
Well, if you read what I said, you will see that its not that easy. You need the complete signal from the last silence to the next silence, so you would have to cache the data and replay it which makes it a little impractical. Also, I don’t know how easy/hard it would be for a DAC to generate this signal even if it had all data it required. But its well suited for pre-calculating and using it as a “perfect” signal and compare it to the output of a DAC.
With a complete measurement like this on real music, it would not be hard to create a “transparency index” which basically tells how close the DAC output is to the original signal. And that would be a very meaningful number to use to compare DACs (can also be used for other HiFi equipment with some modifications).
Caching the digital data is not hard. There are these things called “hard drives.”
Caching the analogue signal is hard. That’s why I asked whether you intended to cache it as bumps on a vinyl disk, or whether you intended to invent some new technology for “caching” the analogue signal for later use.
Yes, you can “pre-calculate” all kind of things. But, then, you have to store the results of your calculation. That’s where all the fun begins…
It’s good to see that someone of your obvious brilliance is hard at work solving that problem.
