[Krassi]

Wow! Thanks for this amazing example!
Lovely!

Seeya !

 

[SoundAndMotion]

By coverage I meant signals measured along with their phase for starters. You can have a different wave with the same harmonic amplitude spectra as a square wave, with the differences being in the relative phase. So when I want to analyse a signal via fft, I expect a complex fft or having both amplitude and phase info. This will also expose in case there are any artefacts in the windowing method used. And in case of timing differences, capturing the exact timing difference, in this case, something at 10us delay and reconstruct within a 44.1khz sampling if it is possible.

Hi @manueljenkin,

Something to play with... The time column is approximate; the sampling rate is 44.1kHz. Each wave is 16-bit integer, and exactly 2 cycles of a sine wave (n.b. you can use a rectangular window), with f=2756.25Hz, and no dither.

In my sheltered little corner of the world, all Fourier transforms give bivariate results (re-im, amp-phase, cos-sin, etc.), otherwise you couldn't investigate the time delays I've introduced. I chose a small number of points in case you want to do it by hand (DFT), otherwise any FFT should allow you to confirm: all waves have the same amplitude and interesting values for time delays. If you want longer records or a .wav file, let me know.

Extra credit: You'll notice that the values in the different columns differ considerably. What is the minimum possible difference? For sine waves, what minimum ∆t does that correspond to?

 

[manueljenkin]

Hi @manueljenkin,

Something to play with... The time column is approximate; the sampling rate is 44.1kHz. Each wave is 16-bit integer, and exactly 2 cycles of a sine wave (n.b. you can use a rectangular window), with f=2756.25Hz, and no dither.

In my sheltered little corner of the world, all Fourier transforms give bivariate results (re-im, amp-phase, cos-sin, etc.), otherwise you couldn't investigate the time delays I've introduced. I chose a small number of points in case you want to do it by hand (DFT), otherwise any FFT should allow you to confirm: all waves have the same amplitude and interesting values for time delays. If you want longer records or a .wav file, let me know.

Extra credit: You'll notice that the values in the different columns differ considerably. What is the minimum possible difference? For sine waves, what minimum ∆t does that correspond to?

Thank you. I'm now looking at those articles first and deriving the full theory (for the whole set of possible aliased signals). For your text, I'll try to do the same for a few other frequencies and multitones. 2756.25 is a perfect multiple of 44.1khz (16x). I'd want to experiment with a non conventional number to make sure there isn't masking of certain phenomenon.

Also the bigger interest will be on the signal that we get after interpolation using sinc filter across the missing points to a fair precision get a visualizable output. Comparing just samples is not an easy job

 

[SoundAndMotion]

Thank you. I'm now looking at those articles first and deriving the full theory (for the whole set of possible aliased signals). For your text, I'll try to do the same for a few other frequencies and multitones. 2756.25 is a perfect multiple of 44.1khz (16x). I'd want to experiment with a non conventional number to make sure there isn't masking of certain phenomenon.

Also the bigger interest will be on the signal that we get after interpolation using sinc filter across the missing points to a fair precision get a visualizable output. Comparing just samples is not an easy job

LOL. I get it.

This is the 6th (and final) version of this post: I keep wanting to give you hints, but realize although we're both "prove it to yourself" types, we still do so in very different ways.
I will mention that the waves I uploaded are also about the 6th versions... I chose every aspect of them to maximize the efficiency for someone like me(!!! - good or bad?) figuring things out. But we are different, so some of my choices weren't appropriate for you.

FYI, when you say "aliased signals", I assume you mean "anti-aliased signals". I usually say "bandwidth limited" (same thing).

Have fun!

EDIT:I hope it's already clear that this is incorrect:

"I thought you were disputing the ability of PCM to represent timing differences less than the sample period" - I am.

 

[manueljenkin]

LOL. I get it.

This is the 6th (and final) version of this post: I keep wanting to give you hints, but realize although we're both "prove it to yourself" types, we still do so in very different ways.
I will mention that the waves I uploaded are also about the 6th versions... I chose every aspect of them to maximize the efficiency for someone like me(!!! - good or bad?) figuring things out. But we are different, so some of my choices weren't appropriate for you.

FYI, when you say "aliased signals", I assume you mean "anti-aliased signals". I usually say "bandwidth limited" (same thing).

Have fun!

EDIT:I hope it's already clear that this is incorrect:

Yeah I was meaning bandwidth limited.

"I hope it's already clear that this is incorrect" - I think you are misunderstanding what I was expecting for a proof. Hope you are aware of things like windowing artefacts, sub Nyquist artifact's (I'm still learning there), and that's where I'm looking to find the proof. As of now, nope, I'm not convinced yet, but I highly appreciate your effort.

 

[SoundAndMotion]

You are already off on your path, and I won't interfere. Pretty sure I know what's in store for you, but... enjoy the trip!

You're right: I don't really know what you're trying to "prove". If you said two-headed people don't exist and I said they do, and you were excited about some papers on genetic and environmental influences on the ontogeny of conjoined twins, and I told you to check out Abby and Brittany Hensel... I assumed you'd say: "aha, I guess they do exist". But you're off into protein-folding and such...
I thought the data I uploaded, showing 5µs and 10µs delays, would demonstrate that RBCD can easily represent such delays. Did you do the FFTs? I think you are hoping to calculate (prove??) the temporal resolution, but that depends on the nature of the signal, as I mentioned before, the peak slope and number of data states. But I guess sub-Nyquist protein folding has your attention.

I understand windowing and leakage pretty well. I'm not familiar with the term windowing artifacts, but I assume it has to do with inappropriate window choices, such as Hamming for transient vibration analysis, which I explained to a reviewer to his satisfaction (paper published). I skimmed the sub-Nyquist artifact article, but it doesn't relate to this discussion. It has to do with the visual appearance of sampled data, such as the pseudo-beats you can "see". Of course you can't hear them; they disappear after proper reconstruction, as per Shannon-Nyquist. Or do you see it otherwise?

I'll leave you alone now, unless you think further discussion seems productive.

 

[bigshot]

 

[D2Girls]

This is the most entertaining thread I have ever had the (mis)fortune to read on head-fi.

 

[gregorio]

[1] I think you are misunderstanding what I was expecting for a proof.
[2] Hope you are aware of things like windowing artefacts, sub Nyquist artifact's (I'm still learning there), and that's where I'm looking to find the proof.
[3] As of now, nope, I'm not convinced yet, but I highly appreciate your effort.

1. I think I too misunderstand what you are "expecting for proof". I've presented a video showing "objective measurement" proof, an experiment you can do yourself that demonstrates the proof, a link to matlab code that demonstrates it, the Shannon/Nyquist Theorem indicates it and SoundandMotion has posted data that proves it. It's hard to imagine what further proof anyone could expect.

2. I am aware, although I don't profess a deep understanding of them. You're going to struggle to find the proof if that's where your looking, especially in the case of "Sub-Nyquist artefacts", which as far as I can tell isn't even related to the encoding and reproduction of sub-sample period delays.

3. It is of course entirely up to you whether or not you're convinced and what proof you personally require in order to be convinced. However, collectively, the Shannon/Nyquist Theorem, objective measurements, the matlab code, repeatable experiments and a lack of any solid/reliable evidence to the contrary is more than enough for science to be convinced. So you appear to fallen into the same "trap" many audiophiles fall into, the same trap you've (rightly) criticised bigshot for, you've made an assertion of fact based entirely on what you personally are (or are not) convinced of, that contradicts the science!

This is the most entertaining thread I have ever had the (mis)fortune to read on head-fi.

Really? I've had the misfortune to read many threads on head-fi that are even more entertaining. I find the Cables subforum in particular to be jam packed with unfortunate and entertaining threads!

G

 

[D2Girls]

I find the topic of headphones vs speakers much more intriguing then cables. Which is why I found this whole thread so interesting.

 

[SoundAndMotion]

sub Nyquist artifact's (I'm still learning there), and that's where I'm looking to find the proof.

Did you work through the Amidror paper? Did you find anything worth sharing?

 

[sander99]

(I moved this from r2r-multibit-vs-delta-sigma-is-there-a-measurable-scientific-difference-thats-audible where it was off topic.)

My concern is both audiophiles and others who think: I know that's false (a lie), so the rest of what bigshot says is/might be too, even if it's true and valuable. And worse, if you and gregorio and castle say mostly the same thing, but they catch your lie, they may discard all 3.

That is exactly what I am concerned about as well. Scientifically minded and well informed people are a minority compared to the people who are misinformed in varying degrees and the latter are exposed to all sorts of marketing bulshit far more than to correct information. For the first group to distinguish themselves from advocating "just another opinion" they should be correct, precise, consistant and complete.

 

[bigshot]

This is the official slag on Bigshot thread. Feel free to do it here to your heart's content. It really doesn't bother me, and if it helps you get it out of your system, so you don't have to pepper your comments in other threads with insults, it has served a valuable purpose. Every time you start out a post with that kind of crap, I stop reading and move onto the next. I rarely read anything from some people because they seem incapable of reining it in. Just wallow in it here where I can ignore it more easily. I'd like to participate in a more constructive manner in all those other threads.

 

[Krassi]

Well some days ago i was irritated by your grumpy comment. But you have a very good point with dealing with hifi religion stuff that mostly begins with "i think that..."
So its a pleasure to read your replies!

 

[bigshot]

GASP! I hope you aren't referring to me!!!