[22906]

   
Your comments on dither would be more accurate if dither was something done after the samples have been obtained, but when done during capture it has a real effect on dynamic range within the main audible band (how else would encodings like DSD function at all?). And any set of samples is not "the original signal", if we define this term as "what went into the microphone".
 
Theoretically, frequency and time are exactly equivalent when conditions are met. In practice, of course, sacrifices have to be made since conditions aren't exactly met. The question therefore becomes one of audibility; that is, can you audibly detect these errors in the time domain that come about by frequency optimizations?

The original signal is absolutely what went into the microphone, and nothing else. Dithering noise can increase dynamic range, but dynamic range is just the difference between the highest and lowest amplitude of the signal. What happens in between the highest and lowest values is what I am calling resolution. And sure, dithering noise can decrease quantization error. I must admit I'm not a DAC designer so I don't know the details of how delta-sigma works. I am approaching the problem from a theoretical standpoint only.

Time and frequency are two completely different measurements. As I noted in a previous post, a time-domain graph can completely describe a signal according to the Shannon Nyquist theorem, but a frequency spectrum cannot (not without phase information). To make the issue about audibility is to remove all science from the discussion.

 

[RRod]

 
The original signal is absolutely what went into the microphone, and nothing else. Dithering noise can increase dynamic range, but dynamic range is just the difference between the highest and lowest amplitude of the signal. What happens in between the highest and lowest values is what I am calling resolution. And sure, dithering noise can decrease quantization error. I must admit I'm not a DAC designer so I don't know the details of how delta-sigma works. I am approaching the problem from a theoretical standpoint only.

Time and frequency are two completely different measurements. As I noted in a previous post, a time-domain graph can completely describe a signal according to the Shannon Nyquist theorem, but a frequency spectrum cannot (not without phase information). To make the issue about audibility is to remove all science from the discussion.

 
There's been plenty of science about what humans can and can't differentiate, both in terms of frequencies and times; so no, making an issue of audibility is not removing science. It's making an actual meaningful benchmark for the end user.
 
As far as phase information, last I checked the DFT basis functions can be transformed between rectangular and polar notation.

 

[22906]

   
There's been plenty of science about what humans can and can't differentiate, both in terms of frequencies and times; so no, making an issue of audibility is not removing science. It's making an actual meaningful benchmark for the end user.
 
As far as phase information, last I checked the DFT basis functions can be transformed between rectangular and polar notation.

I should say it's removing strict objectivity from the discussion. It depends on what your definition of science is.

I think resolution would be almost impossible to quantify in the frequency domain.

 

[castleofargh]

 
What I mean by resolution is how well discrete amplitudes in the input match discrete amplitudes in the output. For an audio signal is completely described by an amplitude-vs-time graph (as the S-N theorem states), but not by a frequency spectrum. This is why resolution must be studied in the time domain.

ok got it. your point is that we'll have more precision at each exact sample point with r2r, and that's probably true(don't know enough in modulation to tell if they bother passing through the exact sample voltage or if it all becomes a bigger math problem where the aim is shaping the wave?).
my trouble with your point is when you take that for better fidelity. how could it be? that's forgetting a little too much about how everything will be wrong between each samples. we're trying to get an analog wave in the end, not the perfect staircases. we're all telling you the same thing here. I call it staircases because I'm a noob, RRod talks about zero order hold, that's the "I know what I'm talking about" way of saying staircases. cjl mentions the same thing as he doesn't understand why you would wish to keep those staircases. and stv014 tries to keep up with your theory, which is courageous as you started wrong and only accept half of what he tries to explain each time.
 
 if you reject noise shaping, anti aliasing, and anything that in the end offers to make the analog output look like an actual wave, what's the point? the original signal was a wave, you certainly don't think you're having the best possible resolution by turning sine waves into staircases?
 
here I also went and did some... how did you call it? independent research ^_^.
http://en.wikipedia.org/wiki/Digital-to-analog_converter
 

 
Piecewise constant output of an idealized DAC lacking a reconstruction filter. In a practical DAC, a filter or the finite bandwidth of the device smooths out the step response into a continuous curve.

from the start you've been saying you didn't want to filter anything. see how that's a tiny little problem?
 
 
but another way to look at it would simply be to ask yourself why they all bother with filters in the first place if it's a bad thing? or maybe you know something the DAC engineers don't?

 

[22906]

  ok got it. your point is that we'll have more precision at each exact sample point with r2r, and that's probably true(don't know enough in modulation to tell if they bother passing through the exact sample voltage or if it all becomes a bigger math problem where the aim is shaping the wave?).
my trouble with your point is when you take that for better fidelity. how could it be? that's forgetting a little too much about how everything will be wrong between each samples. we're trying to get an analog wave in the end, not the perfect staircases. we're all telling you the same thing here. I call it staircases because I'm a noob, RRod talks about zero order hold, that's the "I know what I'm talking about" way of saying staircases. cjl mentions the same thing as he doesn't understand why you would wish to keep those staircases. and stv014 tries to keep up with your theory, which is courageous as you started wrong and only accept half of what he tries to explain each time.
 
 if you reject noise shaping, anti aliasing, and anything that in the end offers to make the analog output look like an actual wave, what's the point? the original signal was a wave, you certainly don't think you're having the best possible resolution by turning sine waves into staircases?
 
here I also went and did some... how did you call it? independent research ^_^.
http://en.wikipedia.org/wiki/Digital-to-analog_converter
 
from the start you've been saying you didn't want to filter anything. see how that's a tiny little problem?
 
 
but another way to look at it would simply be to ask yourself why they all bother with filters in the first place if it's a bad thing? or maybe you know something the DAC engineers don't?

castleofargh:

Let me start off by thanking you deeply for your criticism, without the likes of which scientific progress would not be possible. My response is as follows.

You are confusing "what the waveform looks like" with audio fidelity. No one has the right to say "what the waveform should look like," whether smooth, rough, staircased, sinusoid, or whatever. Visual representation in a graph is but one way of representing the real signal. The basis of the S-N theorem is that there exists something in reality called a "signal" which is independent of the way we choose to represent it (e.g. time domain voltage graph, FFT, sound pressure meter, what have you). My goal is simply to point out that the information contained in the signal is best preserved by a PCM encoding and R-2R conversion process, as sigma-delta conversion "smooths over" details that are present in the PCM encoded signal.

The good DAC engineers (the ones who design high-resolution R2R DACs) DO know this. All I am trying to do is present the information in a way that is accessible to Head-fi readers. Of course a DAC engineer from ____, whose revenue stream depends on fooling consumers into accepting inferior-quality DAC designs, will not ADMIT that this information is true.
 
The zero-order hold is another shortcut, like delta-sigma conversion, that circuit designers have used to simplify implementation, and while it doesn't affect the resolution, it negatively affects the frequency response. The ideal would be to have a Dirac impulse output at each sample of the PCM stream.
 
The fact that I do not approve of extra low-pass filtering, beyond that which is provided by "the finite bandwidth of the device(s)" in question, is something I am personally advocating to improve the current state of the art in hi-fi audio reproduction. By no means am I saying that existing approaches are invalid, just that they may be improved upon.

Here's to further criticism and discussion!
 
- m3_arun

 

[castleofargh]

hehe ^_^.
well on the analog side that is the signal output of a DAC, we do have a voltage value changing in time. so to me it is a perfectly reasonable way to represent an analog signal. a nice little graph with voltage and time, or db and time.
then the fact that we're dealing with the audible range of soundwaves as the original signal we try to recreate, gives us a pretty good idea of the shape the signal should and shouldn't take.
soundwaves are sine waves. music should be a superposition of many different sine waves(else nyquist and his crew couldn't help us). and I can think of very little situations where the end result should be a straight line for any given length of time. and unless I misunderstood, you seem to favor those clean straight lines and rapid value changing of an unfiltered R2R.
that's what I don't understand.
 
about a low pass filter, if we take a CD, it isn't supposed to have above 22khz content, so what reason do you have not to remove all the noise and distortions that the conversion has generated above 22khz? it's obviously improving the signal accuracy to get rid of a part that shouldn't exist.

 

[22906]

The components that follow the DAC, including the wires, active devices, and transducers, will low-pass filter the signal automatically because they all have limited bandwidths. Even that doesn't matter, because ultimately even our ears are low-pass filters.

 

[PowderLegend]

There's no such thing as a staircase output- it's just a graph of the mathematical theory in ADC or DAC. The A part in both of those is still analog.

There's also a simple explanation as to why we don't have more R-2R DACs on the market. They're incredibly expensive to manufacture! Anyone can make and populate a PCB, but to get 20 bits of resolution (a 24 bit DAC) you need to match resistor values to 6 decimal places and they need to be exact across both channels! It's the matching that's expensive. Resistor tolerance is getting better at the rate of Moore's law, which is why we're seeing prices come down on .05% resistors and .01% resistors come to the market. The price of the TotalDac all comes down to the labor in hand-sorting and matching SMD resistors. 

R-2R is a superior DAC method and we'll see better performance and more products on the market as resistor-making technology improves. That's assuming engineers and producers are encoding with SAR ADCs in the first place. 

Let the flame war continue until then. 

 

[castleofargh]

  There's no such thing as a staircase output- it's just a graph of the mathematical theory in ADC or DAC. The A part in both of those is still analog.

There's also a simple explanation as to why we don't have more R-2R DACs on the market. They're incredibly expensive to manufacture! Anyone can make and populate a PCB, but to get 20 bits of resolution (a 24 bit DAC) you need to match resistor values to 6 decimal places and they need to be exact across both channels! It's the matching that's expensive. Resistor tolerance is getting better at the rate of Moore's law, which is why we're seeing prices come down on .05% resistors and .01% resistors come to the market. The price of the TotalDac all comes down to the labor in hand-sorting and matching SMD resistors. 

R-2R is a superior DAC method and we'll see better performance and more products on the market as resistor-making technology improves. That's assuming engineers and producers are encoding with SAR ADCs in the first place. 

Let the flame war continue until then. 

I'm talking staircases kind of signal only because m3_arun wants a R2R DAC without any kind of filtering. so given how fast a R2R DAC could jump to another voltage, the analog output would look a little like staircases. I never thought that my DACs had staircase analog signal output. please don't mistake me for the usual misled high-res fan that uses that kind of graph to try and justify higher sample rates in albums. I'm very much not it.
 

  The components that follow the DAC, including the wires, active devices, and transducers, will low-pass filter the signal automatically because they all have limited bandwidths. Even that doesn't matter, because ultimately even our ears are low-pass filters.

IDK. I'm not sure the "let them be and let's hope they don't come biting us in the ears" is the right universal choice. if all our gears have really low IDM maybe? but why take the risks?
I also have my own beliefs, I think that a low pass filter is important, I think that oversampling is one great way to help on the low pass filter implementation, I think that as long as the measurements are crazy good, as they are on most DACs those days, it's not meaningful to waste money on something giving about the same level of measurements in the end. I also think that amps tend to do worst than DACs, and headphones/speakers even worst, so I don't see why I should complain about the one thing that actually performs the best in my audio system.
all of those ideas as you can imagine, push me far away from looking for the perfect unfiltered R2R DAC. probably why I'm so intrigued and surprised by your own beliefs.

 

[22906]

Of course everyone is entitled to their beliefs; although when great people change the course of history, as Claude Shannon and Harry Nyquist did, I think it is bordering on disrespect to use technology that is based on the knowledge they created, while at the same time defending a view that is in contradiction to that same knowledge.

 

[RRod]

  Of course everyone is entitled to their beliefs; although when great people change the course of history, as Claude Shannon and Harry Nyquist did, I think it is bordering on disrespect to use technology that is based on the knowledge they created, while at the same time defending a view that is in contradiction to that same knowledge.

 
Didn't Shannon show reconstruction via a sinc convolution on the impulse train, which is the same as sending the impulse train through a low-pass filter?

 

[22906]

   
Didn't Shannon show reconstruction via a sinc convolution on the impulse train, which is the same as sending the impulse train through a low-pass filter?

I'm sure he did show that. But I'm also sure Shannon would have understood that audio signals don't require extra low-pass filtering for reconstruction in real audio equipment, and that the phase aberrations introduced by poorly designed filters are more severe than any imagined problems that might result from random ultrasonic frequencies getting to our ears.

 

[RRod]

  I'm sure he did show that. But I'm also sure Shannon would have understood that audio signals don't require extra low-pass filtering for reconstruction in real audio equipment, and that the phase aberrations introduced by poorly designed filters are more severe than any imagined problems that might result from random ultrasonic frequencies getting to our ears.

 
He also understood what it meant to get an exact reconstruction of a band-limited signal. And if these phase aberrations are so bad, then certainly I should be able to pick them up whilst listening to any DAC that doesn't meet your criteria. Regardless, as argh said above, oversampling ameliorates the filter design issues, so you're harping on an old problem.

 

[22906]

   
you're harping on an old problem.

Personal attacks don't belong in this forum. Read the rules.

It doesn't really matter if you think you can "pick up" phase aberrations, they are there, and they are distortions in the signal. My goal is to outline nothing less than an ideal hi-fi audio signal chain.

 

[RRod]

  Personal attacks don't belong in this forum. Read the rules.

It doesn't really matter if you think you can "pick up" phase aberrations, they are there, and they are distortions in the signal. My goal is to outline nothing less than an ideal hi-fi audio signal chain.

 
Saying a problem is old and that you're focusing on it isn't a personal attack, but since you want to play petty, I'll just drop you. Enjoy your ideal chain.