Unless the content is clipped.
Acoustic Guitar , Al diMeola Elysium
"Across the board, his guitar is the focal point, with all backing instrumentation (percussion, keyboards, piano) acting as an accent."
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Let's develop an ASR inter-sample test procedure for DACs!
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Unless the content is clipped.
Acoustic Guitar , Al diMeola Elysium
"Across the board, his guitar is the focal point, with all backing instrumentation (percussion, keyboards, piano) acting as an accent."
Relevant in an absolute sense? Yes. Relevant to the conversation? No.
If the content is clipped, then there's nothing we can do about it so why even bring it up?
I just want to know if my DAC is introducing additional clipping on particularly hot signals. What does that have to do with the Loudness War?
"Well if levels weren't so high to begin with..."
Okay, but levels ARE high. So I want to know if my DAC is introducing additional clipping. As simple as that.
There's theory and there's reality. Most hardware converters use either fixed point or integer math and manipulate samples in the digital domain before conversion to analog. 0dBFS is very frequently the maximum value that can be handled in such devices. Mastering done for consumer devices should consider the practical limitations of such devices. That was my point.
To put it another way:
A NOS DAC is able to reconstruct all digital values to analog without introducing clipping.
An oversampling DAC without sufficient headroom is not able to reconstruct digital values close to or at 0dBFS to analog without introducing clipping.
It's possible to talk about the issue without even mentioning music. Tackling the topic from a purely scientific point of view. Bringing up the Loudness War can help provide context or real-life examples of the issue but that's it.
A NOS DAC is able to reconstruct all digital values to analog without introducing clipping.
An oversampling DAC without sufficient headroom is not able to reconstruct digital values close to or at 0dBFS to analog without introducing clipping.
It's possible to talk about the issue without even mentioning music. Tackling the topic from a purely scientific point of view. Bringing up the Loudness War can help provide context or real-life examples of the issue but that's it.
If it uses a zero order hold, it will just produce a full scale square wave at fs/2 for samples 0 to 200. The rippling is due to bandlimiting to below fs/2.
Anyways, signals with components at fs/2 are not allowed in the sampling theorem because there is an ambiguity about amplitude and phase. For instance,
s_1 = sin(2*pi*fs/2*t + theta)
and
s_2 = sin(theta)*cos(2*pi*fs/2*t)
produce the same samples but are different since s_1 has amplitude of 1 and phase of theta whereas s_2 has amplitude of abs(sin(theta)) and phase of pi/2. This is because
sin(2*pi*fs/2*t + theta) = sin(2*pi*fs/2*t)*cos(theta) + cos(2*pi*fs/2*t)*sin(theta)
and sampling is done at t = n/fs for which the first term is 0 and the second term is identical to s_2 giving the sample values of sin(theta)*(-1)^n for both.
KSTR
Major Contributor
To further illustrate my point (forgive the hand-drawn graphics, I’m not great at math):
Here is a sampled wave (first cycle) going through a zero-order-hold step (second cycle) and finally through a very steep analog low-pass filter (third cycle). This is an ideal representation. As far as I understand, it’s not possible to build a perfect filter in reality. However, the closer a filter is to its ideal version, the more closely the reconstructed wave will resemble its original analog form.
Here is the same sampled wave (first cycle) going through an interpolator/digital oversampling filter (second cycle) and then through the Delta-Sigma modulation step (third cycle). Again, this is an ideal representation. As you can see, since the samples are clipped at the oversampling stage, the Delta-Sigma modulator attempts to reconstruct a clipped wave. If we don’t run the signal through a steep analog low-pass filter at the end of the chain (thus defeating the whole purpose of oversampling), we’ll end up with a clipped wave at the output.
As discussed before, in a real oversampling DAC, things can get even worse, with the digital filter overloading and ceasing to function. So, the example I’ve used here is a best-case scenario.
EDIT: Typos.
Here is a sampled wave (first cycle) going through a zero-order-hold step (second cycle) and finally through a very steep analog low-pass filter (third cycle). This is an ideal representation. As far as I understand, it’s not possible to build a perfect filter in reality. However, the closer a filter is to its ideal version, the more closely the reconstructed wave will resemble its original analog form.
Here is the same sampled wave (first cycle) going through an interpolator/digital oversampling filter (second cycle) and then through the Delta-Sigma modulation step (third cycle). Again, this is an ideal representation. As you can see, since the samples are clipped at the oversampling stage, the Delta-Sigma modulator attempts to reconstruct a clipped wave. If we don’t run the signal through a steep analog low-pass filter at the end of the chain (thus defeating the whole purpose of oversampling), we’ll end up with a clipped wave at the output.
As discussed before, in a real oversampling DAC, things can get even worse, with the digital filter overloading and ceasing to function. So, the example I’ve used here is a best-case scenario.
EDIT: Typos.
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TNT
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It clips and the result is 2nd, 3d etc... but you wont hear the harmonics and the 11kHz that you might hear, will clip - clipping = not being able to play the intended level so, yes, compression... the 11kHz will be heard as a lower level 11kHz - i.e. compression... 3dB compression.
//
Bandlimiting after conversion will not remove any distortion products in the passband. For a symmetrically clipped fs/k signal, harmonics will be odd multiples of the fundamental, 3fs/k, 5fs/k etc. Assuming an ideal rectangular filter just below fs/2, for any k > 6, there will be harmonics below fs/2 and thus in the passband not filtered out. For a filter with cutoff frequency at fc, there will be harmonics in the passband if 3fs/k < fc, i.e. if k > 3fs/fc. For fc = 20 kHz with fs = 44.1 kHz, k > 6.615.
VientoB
Addicted to Fun and Learning
You’re right. Even putting a perfect analog filter after conversion will only fully eliminate distortion for frequencies that are closer to Nyquist. Also, it’s worth mentioning that NOS DACs aren’t perfect. They have issues, but they don’t have to deal with ISOs.
EDIT: Typos.
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VientoB
Addicted to Fun and Learning
I don't understand why only oversampling DACs are affected
John Siau explains the mechanism of this distortion at the beginning of the video I linked in post #449.
See how the wave in the first graph I posted gets “taller” when it goes through an analog filter (when it goes from red to green)? In the digital realm (with digital filters), the same thing happens, the only difference being that we’re dealing with samples instead of voltages. But wait, samples can’t get any higher than 0dBFS (or 1 in the graph), so what happens when they need to exceed that threshold? Well, “ideally” they stay at 0dBFS (second graph) and clip the digital wave, introducing nasty digital distortion (which is bad enough), but as we’ve seen in this thread they can cause the oversampling filter to get overloaded and stop functioning, allowing all sorts of errors to get through.
EDIT: Typos.
EDIT2: You can think of the first graph as a representation of what happens in a properly filtered NOS DAC, and you can pretend the second graph shows you what happens in an oversampling DAC. I’m not an expert so I can’t really explain it further than this. Visualizing what happens with digitally filtered samples can help. See @danadam ’s post below.
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danadam
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With zero-order-hold you need some compensation eq to counteract the roll-off. Otherwise, with Fs/4 tone for example, you'll be short of about 1 dB. See end of this post:
CHORD M-Scaler Review (Upsampler)
Why not just ask watts to supply the test results that substantiate his claims as passionforsound has requested. Say Watts provides an impulse response, would it make us any wiser? Would it answer the question if this IR effectively improves transient timing to the extend that it is audible...
www.audiosciencereview.com
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Hi everyone,
I’m into CD players and discovered only recently the ISO issue.
Here below are my latest THD+N measurements with 3 different ISO test tones. The table talks by itself:
I’ll continue testing.
I’m into CD players and discovered only recently the ISO issue.
Here below are my latest THD+N measurements with 3 different ISO test tones. The table talks by itself:
| Intersample-overs tests Bandwidth of the THD+N measurements is 20Hz - 96kHz | 5512.5 Hz sine, Peak = +0.69dBFS | 7350 Hz sine, Peak = +1.25dBFS | 11025 Hz sine, Peak = +3.0dBFS |
| Teac VRDS-25X | -30.2dB | -24.2dB | -27.9dB |
| Yamaha CD-1 (Non-Oversampling CD Player) | -86.4dB | -84.9dB | -78.3dB |
| Onkyo C-733 | -88.3dB | -40.4dB | -21.2dB |
I’ll continue testing.
Indeed, zero-order-hold has the negative effect to enveloppe the output signal into a sinus cardinal function.With zero-order-hold you need some compensation eq to counteract the roll-off. Otherwise, with Fs/4 tone for example, you'll be short of about 1 dB. See end of this post:
CHORD M-Scaler Review (Upsampler)
Why not just ask watts to supply the test results that substantiate his claims as passionforsound has requested. Say Watts provides an impulse response, would it make us any wiser? Would it answer the question if this IR effectively improves transient timing to the extend that it is audible...
With x=Pi*F/Fc and Attenuation=20*log(sin(x)/x)
So, if F=11025Hz and Fc=44100Hz, we have A=-0.91dB
Source: Oversampling Interpolating DACs
Before anyone asks, no, we're not going back to NOS DACs. Done right, they require S&H and an analog lowpass filter of annoyingly high order (at least 11th) with S&H compensation. Back in the day these were supplied by Murata which has me suspecting ceramic resonators at work (of the high-K variety). Not to mention that this filter will be fixed and we've got a multitude of sample rates to deal with these days. It's just a supremely impractical proposition.
By contrast, dynamic range generally is not in short supply these days, so sacrificing 3ish dB on top is quite feasible if need be.
By contrast, dynamic range generally is not in short supply these days, so sacrificing 3ish dB on top is quite feasible if need be.
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