Basic technical question about digital source signals

In what context, with or without the reconstruction filter. Given there are implementations without one, you can't assume it will be there.

The relevance comes from the fact that the infinitesimally small jaggednesses that any instrumentation can see, if any, is irrelevant to the human ear.

I don't think that is relevant to the discussion or that anyone was questioning what digital can or cannot do, though there was a side discussion on NOS DACs.

Read about Nyquist’s theorem.

Today’s samplers are even higher. Philips (and others) made a study of this during the 70s before the first CD’s were defined and introduced, and used thousands of people in listening experiments to reach a conclusion. No human can tell the difference between a properly sampled and then smoothed signal than an analog one. When the first CDs were introduced, neither the recording nor the playback equipment was as accurate as today. But in the past 10 years or so, the accuracy of ADCs and DACs have improved to an incredible point where noone will be able to tell the difference from the analog signal.

Extremely accurate instrumentation MAY be able to show a difference at a level hundreds of times more sensitive than the human ear. But that is a moot point since 99.9% of the humans will not be able to detect even one tenth of that difference.

Some on this thread will not accept what I am saying. They fall into that 0.1% category or are from another planet :-)

I think there would have to be a "theory of digital audio" at least on reconstruction to break it.


Of course, it also presumes that the subsequent filters are linear.

itsjustme260 posts11-16-2020 9:13am

such a design decision breaks the theory of digital audio.

Not really, it presumes that subsequent filters (mechanical limits in your speakers and your ear, which respond per F=MA; inherent limits in subsequent components) achieve he filtering. There will be no aliasing after the DAC. Yes, there could be HF noise residue; but hearing is highly attenuated above 22 kHz (if present at all) anyway.

Not really, it presumes that subsequent filters (mechanical limits in your speakers and your ear, which respond per F=MA; inherent limits in subsequent components) achieve he filtering. There will be no aliasing after the DAC. Yes, there could be HF noise residue; but hearing is highly attenuated above 22 kHz (if present at all) anyway.

Any presumptive filters won't be ones that do it by the book. HF noise residue most certainly will be present in the absence of an anti-imaging filter.

I would agree that subjectively, having images present is far, far preferable to having aliases.

such a design decision breaks the theory of digital audio.

Not really, it presumes that subsequent filters (mechanical limits in your speakers and your ear, which respond per F=MA; inherent limits in subsequent components) achieve he filtering.  There will be no aliasing after the DAC.  Yes, there could be HF noise residue; but hearing is highly attenuated above 22 kHz (if present at all) anyway.

Just as a design decision not to band-limit the input breaks the theory.

That would truly violate Nyquist's paper.Without band limiting various forms of aliasing and their effects can occur. 

Really quite different

Not broken, a design decision to go NOS without a filter.

Its broken in the sense that such a design decision breaks the theory of digital audio. Just as a design decision not to band-limit the input breaks the theory.

Given the number of people who prefer nonoversampled DACs something seems wrong/incomplete with this theory

Well, first, i’m providing a technical answer. You need not like it, but it is true.

Next, people have many opinions. Many are odd. Many will disagree. Look at politics.

Third - done right i clearly DO like it, ad anyone who listens to bitstream or DSD is listening to hugely over sampled streams by definition.

Fourth - we have no idea what was done in the anti-alias filter; that occurred in the studio. oversmapling was almost certainly employed, statistically, but we don't know. And aliasing is NEVER a good thing. It creates (maybe) tones that never existed in the first place.

I cannot personally imagine how allowing hgih frequency junk through, or having brick-wall,phase incoherent filters can possibly be preferable, but hey.
G

You are equating accuracy with preference. That never ends well in the audiophile world.  People will make up all kinds of justifications why their preference is "more accurate". But the key phrase here is "make up".

Given the number of people who prefer nonoversampled DACs something seems wrong/incomplete with this theory

itsjustme
When you over or up sample a signal the goal is not to magically create missing information from a vacuum. Its simply to move the noise ("steps") to a higher frequency so that they are more easily filtered out. Get i hgih enough and your ear will do it on its own.
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Given the number of people who prefer nonoversampled DACs something seems wrong/incomplete with this theory

https://www.stereophile.com/images/712an.AN41fig03.jpg

Not broken, a design decision to go NOS without a filter.

https://www.stereophile.com/content/holoaudio-may-level-3-da-processor-measurements

Or in this case, the option to run NOS or not without a filter.

headphonedreams

You can actually see small steps in Stereophile's measurements of many dacs.

Which ones? It's a broken DAC if you can see steps on the output.

So, the quick answer is it is smoothed. Yes, there are discrete samples. But filters reconstruct the analog wave form, essentially via low pass filtering.  At the recording studio a similar set of filters is in place to ensure that nothing above the cut-off frequency (let's not get too deep here) is captured -- which can mess up the entire process.
Basically this si what a DAC does.  It converts Digital to Analog. There are different methods, but step #1 is to create a PDM or PAM output (one's a stair-step, one varies the density of equal height pulses just like fuel injection). The 2nd step is to smooth it out and remove the hgih frequency noise.  All of this was figured out int he 1960s, mostly at Bell Labs for long distance telephony.

The results are very good, but nothing is perfect. The analog amplifiers and filtering were among the first places addressed for improvement when digital first came out int he 80s. Not only are analog filters in place, but nearly everyone uses digital filters on an over-sampled signal.
When you over or up sample a signal the goal is not to magically create missing information from a vacuum. Its simply to move the noise ("steps") to a higher frequency so that they are more easily filtered out. Get i hgih enough and your ear will do it on its own.
You can perform normal measurements  - noise, distortion, etc on a the analog output of a DAC.
G

You can actually see small steps in Stereophile's measurements of many dacs.

Playing 24/96 gives much, much smaller steps if the source has the info and the dac has the resolution. Most dacs can only differentiate up to around 20 or 21 bits. 20/96 still has step heights 16 times smaller than 16/44 (and a bit less than half the width).

Give me a moment..............

I was thinking when playing PCM through Sigma Delta but pure DSD path would look steppy but much smaller steps since still discrete in time.

From a practical standpoint, depending on the Reconstruction filter, whether there is one or not, DSD will still stair step because it is reproducing PCM values.

PCM stairstepped.
DSD not.
But you usually have to spend up to play pure DSD. Most systems use DOP.

google "digital to analog conversion' and 'nyquist theorem'

The output of a DAC sans built in filter or external filter will be a stairstep. I can't think of a DAC in audio that is not convert and hold.


gs5556, that is a conceptual answer, not the reality of an actual DAC. Not many (any) DAC have an impulse function output.

You will see an analog waveform. There is no such thing as a digital stair step waveform because a digital signal does not have a defined value between two points in time. It has only one discrete point, and that point in time is the instantaneous sample point. The "starstep" draws a line between two sample points, or it draws a line where the signal does not exist. It is just a picture created on paper to visualize a digital signal.

Cleeds,

In that video, he is showing the output of a DAC with an analog reconstruction filter. It is filtering out the stair-steps. Which goes back to my post, on most DACs, there would be no stair-step evident. On non oversampling DACs or any DAC without an analog filter, there would be evidence of stair-steps.

berner99

... if you look at the output from a digital source e.g. on an oscilloscope, would it appear "smooth" i.e. has all the stairstepping that occurs when you convert digital to analog been smoothed out or would the signal appear jagged to some extent?

The "stairstepping" you refer to is really a misnomer, although it's widely believed. For proof, see this.

Berner99 on most DACs it would look smooth. There is a trend on most audiophile non oversampling DACs not to have an output filter. Depending on the bandwidth of their analog electronics in those DACs, it would either look much like a staircase or a staircase with rounded edges.

You're thinking that since digital samples values at different points that when played back its a string of discrete points instead of a continuous curve. That's not the way it works. Whether played back through an amp or viewed directly from a player to a scope it will always look nice and smooth.  

Just one in a very, very long list of reasons why specs, scopes and measurements are inferior to a good set of ears.