Yes, the theoretically ideal sample is an Dirac impulse. So, infinitely narrow, with infinite amplitude. In the real world of finite existence, a DAC's output steps have finite width and can operate Return-To-Zero (RTZ), or Non-Return-To-Zero (NRZ). RTZ is closer to a Dirac impulse, yet, as you observed, it simultaneously results in both the strongest image-bands and the poorest SNR.
NRZ DAC operation on the other hand, which is pretty much ubiquitous, creates an image-suppression masking effect (a SINC shaped comb-filter effect). This providences somewhat suppressed image-bands, and a better SNR, than with RTZ. It also, however, is what causes the -3dB @ 20KHz response droop of most NOS DACs. By the way, this masking effect is present in NRZ OS DACs as well, it's just not as severe due to OS moving the droop's location up in frequency by a factor equal to the OS ratio. In addition the droop is digitally EQ's flat within the interpolation filter.
I don ' think non over sampling is sounding better, but more than the added circuitry may more harm than it helps often, at least for the generation of old pcm chips such a question is often related in mind.
Whatever the reason : extra jitter, less proof layout, more active devices chips between the signal and the dac chip. all of that often may suppress a transparency, of, at least less neutral to my -maybe biased- ears.
I believe the subject shouldn't be asked without the question of added filters, anyway I see up and over sampling operations by nature as a filter
The question should be evaluated again if talking about old pcm chip according the better hardware and knowledges gained about DAC device and layout over the interogation that has begunn iirc with the japan audio company 47 Lab. something.
Just my two cents as havent read the whole thread yet.
Whatever the reason : extra jitter, less proof layout, more active devices chips between the signal and the dac chip. all of that often may suppress a transparency, of, at least less neutral to my -maybe biased- ears.
I believe the subject shouldn't be asked without the question of added filters, anyway I see up and over sampling operations by nature as a filter
The question should be evaluated again if talking about old pcm chip according the better hardware and knowledges gained about DAC device and layout over the interogation that has begunn iirc with the japan audio company 47 Lab. something.
Just my two cents as havent read the whole thread yet.
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The mathematically correct reconstruction filter is a SINC function.
For upsampling, take a look at the PGGB utility.
PGGB - Offline remastering
I went to the PGGB website and saw some interesting things there. Until, I also saw that the private (non-commercial) use licensing fee was $500!
you have my point why. Technically I have no exact clue, but grossly I would think each time you put something between the enter and the output of a signal, you have a sounding change, whatever what is : layout, change, active parts change, passive part change, volt/current parameter change and so on. It's what about a filter is, electrically it changes enough for the ears to be noticed and ears seems to be sensible enough, more than the usual steps we are discussing : is there a life below 5° harmonic and so on, etc ? I think there is, but it's difficult to quantifiable and reproduce to extract a tool precise enough for the technician in order to reproduce and rule the sound effects he is wanting... I mean in the last % of what is a sounding good enough device according to mass market others. Cause at the end this is exactly what we discuss.
Your question imho makes only sense to know where it's sounds better - i.e. isolate the effect in order to shape the sound-, it's often hard to isolate each time the reason why and make generalizations more than the ones that are each time involved : jitter, noise, THD, filters. It's not enough imho locally when you refere at a sound change that is a whole of several devices that interacts and that make the life hard to the designer to isolate and rule every aspects of those change in relation to each others.
At the end a perfect list of ruled concepts can sometimes make the result not as good one wants, while of course it is the needed starting point.
The trap being to pick up always in that list to involve the change in sound. The usual lists of that technical rules are mandatory but not enough.
Being about oversampling I stay about what I said firstly : you introduce something, the ears are sensitive enough to hear it what ever the subjective about nice or not.
my 2 cents as I can NOT discuss the direct effect of the oversampling filter more than that. I assume, it's relative to an area of the ears that is sensible to the aliasing and such artifact of the numeric recording that the ears can check. But not able to say what ! Phase ? I sincerly dunno.
Your question imho makes only sense to know where it's sounds better - i.e. isolate the effect in order to shape the sound-, it's often hard to isolate each time the reason why and make generalizations more than the ones that are each time involved : jitter, noise, THD, filters. It's not enough imho locally when you refere at a sound change that is a whole of several devices that interacts and that make the life hard to the designer to isolate and rule every aspects of those change in relation to each others.
At the end a perfect list of ruled concepts can sometimes make the result not as good one wants, while of course it is the needed starting point.
The trap being to pick up always in that list to involve the change in sound. The usual lists of that technical rules are mandatory but not enough.
Being about oversampling I stay about what I said firstly : you introduce something, the ears are sensitive enough to hear it what ever the subjective about nice or not.
my 2 cents as I can NOT discuss the direct effect of the oversampling filter more than that. I assume, it's relative to an area of the ears that is sensible to the aliasing and such artifact of the numeric recording that the ears can check. But not able to say what ! Phase ? I sincerly dunno.
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Reconstruction filter is a mathematical guessing on what is "missing" in the sound pattern. This prediction sometimes hits the spot and sometimes it doesn't. This abnormal hit can sound like a detuned instrument (OS), which is worse as a missing tone (NOS). The missing tone is physically feathered on the way to the ear (speaker/headphone membrane movement), and therefore the NOS is more natural from the impression (without unreal artifacts, exact tones are maintained).
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The guessing of the reconstruction filter (magnitude of intermediate samples between the known samples) is always better, than the zero-order S/H, or even the first order S/H. The higher is the order of the filter polynom, the better is the guessing. In principle OS should sound better, if we consider only this aspect.
I find it much easier to gain a conceptual understanding of what a DAC's interpolation filter does when its operation is viewed in the frequency-domain, rather than the time-domain. A time-domain view, is how the signal would appear on an oscilloscope display, while the frequency-domain view is how it would appear on a spectrum analyzer display. In the time-domain, interpolation appears as a continuous sequence of sample points, inserted to fill-in missing data implied by whatever sample points were provided by the originally sampled signal. Except, I don't think that's best way to conceptually think of what the interpolation filter does. What it actually does is more easily understood when the DAC's output signal is viewed in the frequency-domain.
In the frequency-domain, we see that the un-reconstructed DAC output already COMPLETELY contains the full desired signal band - known as the baseband. It's just that it's accompanied by repeating copies of itself, extending up in frequency, and which start no lower than 22KHz for CD format. These repeating copies are known as image-bands. The image-bands disguise the fact that the complete desired signal band is already present when viewed only in the time-domain. Interpolation and low-pass filtering are two sides of the same coin. They are the same operation. Low-pass filter the image-bands, and additional points are interpolated which make the signal more smoothly continuous. Interpolate the signal, and the image-bands disappear, thus also making the signal more smoothly continuous. Same, same.
The image-bands are what make a DAC's un-reconstructed output signal discrete looking, as opposed to smoothly continuous looking. So, the signal reconstruction function is at once interpolation when viewed in the time-domain, AND low-pass filtering when viewed in the frequency-domain. It now becomes more obvious that to reconstruct the original signal band, all need be done is to fully remove (low-pass filter) the image bands. Seen this way, we aren't led to think of the reconstructed signal as being mathematically "guessed" at via interpolation. We can see that interpolation is actually performing a low-pass filtering operation. Yes, that too, uses math computation. Let's not forget that these are sampled digital signals, which are inherently numerical.
So, a digital reconstruction filter doesn't really "guess" at samples missing from the original signal. It, instead, determines which additional samples are necessary to filter away the image-bands. That said, it is possible that the original sample values may be relocated in that process. It's also possible to design the the filter to leave the original values untouched.
^^^
An excellent approach IMHO. And a novice question from my side: Let's assume we could remove the images in a manner that does not affect the audio band in the digital or analog domain. Just say we cut the images in a magic way so that the "staircase" waveform of the un-reconstructed signal stayed as is. Could this ever happen, or the staircase will reproduce the images once again? Does theory predicts anything about this?
An excellent approach IMHO. And a novice question from my side: Let's assume we could remove the images in a manner that does not affect the audio band in the digital or analog domain. Just say we cut the images in a magic way so that the "staircase" waveform of the un-reconstructed signal stayed as is. Could this ever happen, or the staircase will reproduce the images once again? Does theory predicts anything about this?
@MagicBus,
If I correctly understand your question, then the answer is, no. The image-bands cannot be removed while leaving the DAC analog signal discrete (not reconstructed) - leaving aside the question of why you would want to. The image-bands are THE reason why the DAC's output is discrete rather than continuous. Remove the image-bands, and the signal MUST become a continuous waveform containing only the original desired signal band. The signal then becomes, by definition, reconstructed.
If I correctly understand your question, then the answer is, no. The image-bands cannot be removed while leaving the DAC analog signal discrete (not reconstructed) - leaving aside the question of why you would want to. The image-bands are THE reason why the DAC's output is discrete rather than continuous. Remove the image-bands, and the signal MUST become a continuous waveform containing only the original desired signal band. The signal then becomes, by definition, reconstructed.
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My 2 cents on this.
So far all talk and discussions as well as testing regards how all the system responds to a sine wave. But music as seen through an oscilloscope is more like a bunch of random patterns that don't quite repeat itself accurately.
It is virtually unknown how a reconstruction filter will actually operate on the signal. In a NOS you can be assured that in the mathematics, the line between two points will be a curve of sorts.
In a reconstruction filter, the values can be any number. Therefore the possibility of it making a gross error is significantly higher.
Nobody has actually done a test to say it can reconstruct a musical signal more accurately. It has only been proven that it can reconstruct sinewaves more accurately. Although some would argue that the musical waveform is a super position of multiple sinewaves. I believe the truth is much more complicated then that.
I heard some really lousy OS DACs as well as good ones. But NOS DACs are generally quite okay.
I remember reading somewhere of a person trying out various filter configurations to compare sound quality, his conclusion was that a filter that is not too steep is the answer and is better than NOS and a brick wall filter.
In short, what I am saying is the guesses in the reconstruction filter becomes a hit and miss once you feed in real music signals and is highly dependent on implementation, whereas for NOS, the error is significantly less and is something that we find more tolerable especially in the midrange and bass frequencies where the error is small.
Oon
So far all talk and discussions as well as testing regards how all the system responds to a sine wave. But music as seen through an oscilloscope is more like a bunch of random patterns that don't quite repeat itself accurately.
It is virtually unknown how a reconstruction filter will actually operate on the signal. In a NOS you can be assured that in the mathematics, the line between two points will be a curve of sorts.
In a reconstruction filter, the values can be any number. Therefore the possibility of it making a gross error is significantly higher.
Nobody has actually done a test to say it can reconstruct a musical signal more accurately. It has only been proven that it can reconstruct sinewaves more accurately. Although some would argue that the musical waveform is a super position of multiple sinewaves. I believe the truth is much more complicated then that.
I heard some really lousy OS DACs as well as good ones. But NOS DACs are generally quite okay.
I remember reading somewhere of a person trying out various filter configurations to compare sound quality, his conclusion was that a filter that is not too steep is the answer and is better than NOS and a brick wall filter.
In short, what I am saying is the guesses in the reconstruction filter becomes a hit and miss once you feed in real music signals and is highly dependent on implementation, whereas for NOS, the error is significantly less and is something that we find more tolerable especially in the midrange and bass frequencies where the error is small.
Oon
The staircase and the images are one in the same (high frequency content - Fourier analysis).
I just spent four paragraphs in post #29 explaining how none of the above notions are correct.
I didn't find it lost any of the positive NOS characteristics when upsampled 2X. But there is a bit of a caveat caused by the change in FR when upsampling - it can sound like the upsampled DAC has more 'air' or improved transparency in HF but this effect is most likely caused by the reduction of the NOS droop at 2X.
For me the biggest weakness of NOS was uneven HF which would manifest (for example) as 'clanginess' on close-mic'd piano. As my listening diet includes a large proportion of solo piano this was a significant drawback for NOS. It got solved by implementing the LC reconstruction filter - the degree to which it was eliminated depends on the filter's steepness. 3rd order improves it but doesn't completely eliminate it, 7th order eliminates it to the degree that so far I haven't noticed any improvement when going to 9th order.
OS is unable to reconstruct the original waveform due to the recent loudness war. I'm sure it can't get rid of ISO(Inter Sample Overs). What you hear isn't a true OSed sound. NOS never has ISO as long as post-LPF is enough margin(usually it has). If you compare true OS(without ISO) with NOS, it's better to have -3dB attenuation to avoid ISO.
My NOS designs don't - why compromise for the 'legal' users of PCM to accommodate the 'illegals'? The 'illegals' can simply apply digital attenuation before the DAC. Btw 3dB attenuation isn't always sufficient, worst case I've seen approaches 6dB.
Transformers are good... if used straight after a DAC IC, they filter out the very high-frequency rubbish coming from the DAC's... and they do this with the least amount of harm possible, compared to active stages doing the same thing. They give most, introduce the least amount of harm... and they just sound so right.
They also have a very nice high freq. roll-off which is, in the case of digital audio, in fact, a desirable characteristic. Not to mention the silicon (IC/OP amps)-free stage, to get from differential DAC-out, to single-ended (RCA's) out in a straightforward manner. They will sound nice, but not measure nice.... and these days, it's all about the measurements...
They also have a very nice high freq. roll-off which is, in the case of digital audio, in fact, a desirable characteristic. Not to mention the silicon (IC/OP amps)-free stage, to get from differential DAC-out, to single-ended (RCA's) out in a straightforward manner. They will sound nice, but not measure nice.... and these days, it's all about the measurements...
This is exactly what I needed to clarify, thanks!
Thanks! Trying to bring all this down to my simplified "analog" model, the question arising is if the images are the result of the missing points between the "stairs" or the rising time -thinking square wave test.
I've seen your posts with measurements of the frequency response correction with passive filter. Any chance you have captured the filtered output with an oscilloscope to evaluate possible reconstruction/interpolation as well?
In this post from last year I show two versions of an 18kHz sinewave output by my DAC on my 'scope. The first is with a 3rd order reconstruction filter, the second with a 7th order. The significant image frequency is at 26.1kHz which is quite well suppressed on the 7th order filter.
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