DAC types and their sonic signature

[solderdude]

Superposition of Waves

The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any point in space or time, is simply the sum of the individual wave displacements. This is true of waves which are finite in length (wave pulses) or which are continuous sine waves.

 

[pkane]

It's a 'sum' of oranges and apples. You sum two oranges and three apples, what do you get as a sum? A collection of two oranges and three apples. You don't get 5 'orangeapples'.

I edited my previous response and added a question.

You are thinking about it all wrong. F1 and F2 don't exist independently in a recording. Precisely one signal is captured, regardless of how many frequencies it contains, and it is the SUM of their respective amplitudes over time. Stop being lazy and read up on some of this stuff, it'll be enlightening.

 

[March Audio]

Tell me, why is it so hard to understand that different frequencies don't blend?
You can't sum amplitudes of various frequencies. It's just a graphical representation. It never happens in reality. They stay appart with each of them holding their own amplitude.

OMG. You have clearly never used an oscilloscope. You seem to have a fundamental misunderstanding of time domain and frequency domain representation. An ADC captures the instantaneous time domain amplitude values at the respective sampling points. It knows nothing of the discrete signals the waveform contains.

Two sine waves, 1 kHz and 4 kHz both at -12dBFS

you can even see those points if you zoom in

 

[zalive]

You are thinking about it all wrong. F1 and F2 don't exist independently in a recording. Precisely one signal is captured, regardless of how many frequencies it contains, and it is the SUM of their respective amplitudes over time. Stop being lazy and read up on some of this stuff, it'll be enlightening.

You're dealing with the terminology. Call it what you will, it's not important. Those waves don't blend. That's what's important.
Superposition principle tells that f1 and f2 are independent. This is the reason why term superposition is used.

 

[pkane]

You're dealing with the terminology. Call it what you will, it's not important. Those waves don't blend. That's what's important.
Superposition principle tells that f1 and f2 are independent.

This is completely meaningless. Can you point out to me each of the individual frequencies, since they "don't blend"? Seems to me they are blended pretty well...

This is from an actual digital recording:

 

[Krunok]

You're dealing with the terminology. Call it what you will, it's not important. Those waves don't blend. That's what's important.
Superposition principle tells that f1 and f2 are independent. This is the reason why term superposition is used.

@Thomas savage Don't you think this has become ridiculous enough to end it?

 

[March Audio]

It's a 'sum' of oranges and apples. You sum two oranges and three apples, what do you get as a sum? A collection of two oranges and three apples. You don't get 5 'orangeapples'.

I edited my previous response and added a question.

There couldnt be a more incorrect analysis. Its such a fundamental lack of understanding that I strongly suspect its actually just a wind up.

 

[zalive]

2 sine waves, 1 kHz and 4 kHz both at -12dBFS

you can even see those points if you zoom in

It's a representation given by oscilloscope.

This is completely meaningless. Can you point out to me each of the individual frequencies, since they "don't blend"? Seems to me they are blended pretty well...

You showed a representation which sums them, and conclude they blended in the nature. They didn't. Frequencies stay apart.

 

[solderdude]

What Zalive is saying is true in his p.o.v.

take the plot below

Suppose the 2 tones are added sonically the resulting sound wave would be a superposition (summation).
The sound pressure at the mic position would be exactly as the plot below shows.
When the 2 tones were 'mixed' they would be summed and the result would be the same (there is no difference)
There is only 1 waveform... the summation (Zalive likes to be different and calls it superposition).
When we listen to that waveform we hear 2 distinct frequencies from that one waveform.
I suspect this is what he means.

Blending is when you mix 2 (or more) things which results in something new that cannot be separated or easily discriminated as the originals.
The signals don't blend.
They sum (superimpose)

semantics

blending is something you do with a mixer:

or you can mix with a blender

The audioequivalent of blending would be to mix (sum or superimpose) say 3 or more music recordings that sound very different.
That would blend and result in a bunch of instruments that may or may not be told apart anymore and the essence (the melodies) would be lost as the brain nor electronic wizardry cannot tell the instruments or recordings apart anymore. (except with nulling using the original recordings)

 

[pkane]

It's a representation given by oscilloscope.

You showed a representation which sums them, and conclude they blended in the nature. They didn't. Frequencies stay apart.

But wait, this is recorded from a natural signal. How could that possibly be if the waves don't sum together? How do you think all these waveforms got blended? Did I do something wrong in capturing it?

 

[zalive]

What Zalive is saying is true in his p.o.v.

take the plot below

Suppose the 2 tones are added sonically the resulting sound wave would be a superposition (summation).
The sound pressure at the mic position would be exactly as the plot below shows.
When the 2 tones were 'mixed' they would be summed and the result would be the same (there is no difference)
There is only 1 waveform... the summation (Zalive likes to be different and calls it superposition).
When we listen to that waveform we hear 2 distinct frequencies from that one waveform.
I suspect this is what he means.

Blending is when you mix 2 (or more) things which results in something new that cannot be separated or easily discriminated as the originals.
The signals don't blend.
They sum (superimpose)

Yess solderdude. Finally. This is what I mean, yes.
I can accept the term sum, after all if I'm honest I used it myself previously in this thread. Superposition is the term I was taught related to the subject.

Oscilloscope measures all the frequencies present, it sums the response of all frequencies.
But in nature each frequency stays apart, separate from the rest of the frequency band.
Because of this, looking at oscilloscope graph may give a false impression. 2D representation in oscilloscope graph visually blends those frequencies.
When you look at filterless waveform, graph won't show that the sine of the fundamental tone is present in this graphical mess. But it is, there is the sine of that tone in its perfect shape, but graph sums it up with those ultrasonic frequencies, and the resulting graph is stepped.
And how we know that the sine of the tone is there? Because a single wave of a single frequency can only be a sine. The nature of vawes.
So if there's a frequency present, its sine is present there.
Those ultrasonics are varying pulses of various higher frequencies, hence the difference between neighbouring cycles of the base tone.

Possibly I struggle in explaining in english when I try to describe what I want...

 

[zalive]

But wait, this is recorded from a natural signal. How could that possibly be if the waves don't sum together? How do you think all these waveforms got blended? Did I do something wrong in capturing it?

Oscilloscope measures resulting (total) voltage in the time domain, It doesn't discern frequencies which constitute the signal.

 

[Krunok]

When we listen to that waveform we hear 2 distinct frequencies from that one waveform.

Sure we do, but that is ablity of our brain to extract individual tones and not a prove that 2 waves were not summed up.

When you watch 10 kids play your brain can easilly extract individual voices although all 10 voices has been summed up, so this abilty of brain also works with complex soundforms like voices, not only with sine waves. Guys, this is hardly a rocket science..

 

[solderdude]

Oscilloscope shows a waveform.. it does not care if it is a summation or not.
It merely plots the measured voltage over time.
There is nothing more to it.

You are incorrect in your assumption about the sample-and-hold being the same as sample points in time.
To reproduce sample points in 'real time' you would need an infinite bandwidth and you would hear nothing because of it as the, very shortly in time existing points, would be there and gone so fast the eardrum would not even move.
So one can resort to PWM, PDM or PCM for instance to (re)create an actual voltage.
In R2R this is done by a technique called sample-and-hold.
These are the stairsteps.

The error in your thinking is that the stairsteps are merely a 44kHz squarewave (with a differing amplitude) that is superimposed on the waveform that is to be reproduced.
It isn't.
You need to realize that the waveform (the pure sine) is 'described' by the samples but the waveform is not embedded in the samples.

The filterless DAC thus does NOT produce a pure sinewave (the described one) + 44kHz squarewave with its harmonics, otherwise it would not be a squarewave.
It produces sample values that last 1/44,100 of a second.
For lower audiofrequencies the waveform consists of many very small steps that merely produce small and inaudible amplitude errors.
The problem begins at higher frequencies. There are less sample points per period of the frequency. Also the sampling frequency and that of the ones in music are NOT synchronised.
This results in not enough sample points to describe the high frequency sine wave.
An R2R chip can only reproduce voltage levels, not points nor can is estimate what the original shape was.
For this the output voltage is a raw signal that needs more processing.
For this the reconstuction filter is needed.
It is mandatory and not optional and not merely a steep lowpass filter.
It must have the correct Q and steepness for the original waveform to remerge again.
Get the Q wrong and the FR is off and attenuation too little (stairsteps show)
Get the frequency wrong and the FR is 'off'. Either too low and cutting in the audible band or too high and stairsteps appear as well as the higher frequencies not being described 'accurately' any more.

 

[solderdude]

Sure we do, but that is ablity of our brain to extract individual tones and not a prove that 2 waves were not summed up.

Indeed, just explaining what Zalive meant... In fact you can easily filter them apart again and look at the FFT to see that there are 2 different frequencies with their own amplitudes. That is when there is no harmonic and IM distortion around

When you watch 10 kids play your brain can easilly extract individual voices although all 10 voices has been summed up, so this abilty of brain also works with complex soundforms like voices, not only with sine waves. Guys, this is hardly a rocket science..

It is easy to separate when you are watching them. It becomes harder to do when you listen to a recording or without watching. It would be impossible to separate those voices from each other using an FFT or other forms of measurements in audio electronics.
When they are all singing or speaking the same at the same volume even the brain cannot separate them... but we do like to think we do when watching someone in a choir sing.

The brain and its input (localization, think HRTF, eyes ) and the complexity of the brain allows you to 'separate', an analyzer can not.

But all of this has nothing to do with DA conversion and the essential reconstruction filter.
The above is about perception, acoustics, emotions and visual confirmation.

 

[March Audio]

It's a representation given by oscilloscope.



You showed a representation which sums them, and conclude they blended in the nature. They didn't. Frequencies stay apart.

Yes it is the time waveform as would be received by a microphone. It contains the entire frequency content if the signals. What's your point?

 

[March Audio]

Oscilloscope shows a waveform.. it does not care if it is a summation or not.
It merely plots the measured voltage over time.
There is nothing more to it.

.

This

 

[March Audio]

What Zalive is saying is true in his p.o.v.

take the plot below

Suppose the 2 tones are added sonically the resulting sound wave would be a superposition (summation).
The sound pressure at the mic position would be exactly as the plot below shows.
When the 2 tones were 'mixed' they would be summed and the result would be the same (there is no difference)
There is only 1 waveform... the summation (Zalive likes to be different and calls it superposition).
When we listen to that waveform we hear 2 distinct frequencies from that one waveform.
I suspect this is what he means.

Blending is when you mix 2 (or more) things which results in something new that cannot be separated or easily discriminated as the originals.
The signals don't blend.
They sum (superimpose)

semantics

blending is something you do with a mixer:

or you can mix with a blender

The audioequivalent of blending would be to mix (sum or superimpose) say 3 or more music recordings that sound very different.
That would blend and result in a bunch of instruments that may or may not be told apart anymore and the essence (the melodies) would be lost as the brain nor electronic wizardry cannot tell the instruments or recordings apart anymore. (except with nulling using the original recordings)

Yes but its so semantic and pedantic that I can only see it as a wind up to argue about it.

I think he is another for ignore, life is too short.

 

[zalive]

Oscilloscope shows a waveform.. it does not care if it is a summation or not.
It merely plots the measured voltage over time.
There is nothing more to it.

It doesn't care what is there, it measures voltage over time and it represents values as measured point by point. Again you know a lot better a practical side to the oscilloscope, but the principle is as you described it here. Its task is to create a value vs time graph.

The error in your thinking is that the stairsteps are merely a 44kHz squarewave

But I never said those are squarewave. I used the squarewave as an example to describe Fourier analysis.
Yet Fourier tells you would still be able to recreate the filterless waveform pattern as shown on oscilloscope, by using a sampled tone sine plus sines of various higher frequencies.
As this waveform changes with time as seen from the graphs you'd need some pulses of sine to get the right waveform.
Obviously ultrasonic garbage are various pulses rather than continuous.

The filterless DAC thus does NOT produce a pure sinewave (the described one) + 44kHz squarewave with its harmonics, otherwise it would not be a squarewave.
It produces sample values that last 1/44,100 of a second.

DAC will produce a correct frequency for the sampled tone. Thanks to Shannon-Nyquist and sampling frequency used in practice, it's ensured within 20kHz bandwidth.
You can't get 'sample values' from the analog stage (output) after the DA is done. You get frequencies of analog signal out of the DA.
In ideal scenario you'd get just a sine wave of the sampled tone. In a real world, out of the analog stage you get a sine wave of the sampled tone, plus ultrasonic garbage.
And when you measure it with the oscilloscope you'll measure both the tone signal and the garbage summed up, and it will look like what it looks like.

All this is why applying a simple steep LPF to the output will 'recreate' the sine. Filter out ultrasonic and there it is the sine wave of the tone.
But in my view recreation it's just a colourful way of describing what happens. Sine wave gets recreated at the oscilloscope. While in reality sine wave of the tone is already there and doesn't have to be mended itself.

 

[zalive]

The brain and its input (localization, think HRTF, eyes ) and the complexity of the brain allows you to 'separate', an analyzer can not.

Yes. An analyzer gives a 2D graph with all frequencies waves blended in a sum result - in the graph. Oscilloscope doesn't discern frequencies apart.