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# 24bit vs 16bit, the myth exploded! - Page 113

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Originally Posted by SilverEars

What is Pickle's nationality?  Breed? Is it a mut?

She is a Pomeranian... also known as a German Spitz.

Quote:
Originally Posted by ab initio

Got a picture of a tweeter?

this one is my tweeter... Schlitzee. She is a PomChi (half pomeranian half chihuahua)

Quote:
Originally Posted by groovyd

Having passed my masters in digital signal processing with flying colors I respectfully disagree with you and that link.  I can easily fit an infinite number of near sine waves into a set of samples at twice its frequency without even introducing the concept of sample phase.  Introducing sample phase gives me yet another infinite set of this time absolutely perfect sine waves to choose from.  Of course this assumes nobody cares about phase either in addition to amplitude.  In fact, as sample phase approaches integer multiples of pi the variety of near-perfect sine waves that fit the samples approaches infinity.  What this means is your filter must be dead nuts perfect to even have a chance of reconstructing one of an infinite number of phase shifted sine waves that 'might' be correct but absolutely is not with inverse probability to sample phase.

Sure, mathematically only one wave fits if: 1) sample phase is not a multiple of pi and 2) it is an absolute perfect sine wave and 3) you are assuming perfect brick wall filters with zero phase shift.

Unfortunately none of these conditions even remotely represent a real system in any way.  Yours is a straw man argument that I won't argue with anymore... you can make believe whatever you want.

What parts in the video do you disagree with?

And how is any of the above relevant to 44.1 kHz as Nyquist frequency being adequate for (human... sorry dogs!) audio applications?

Quote:
Originally Posted by esldude

Don't know what you imagine I am imagining, but it appears you are crossed up on it there.  Two sine waves of the same frequency will add to a larger or smaller wave of the same frequency depending on the amount out of phase they are.  At 180 out it goes to nothing, and at 360 or multiples it is doubled up.  If it happens at 22 khz I won't hear it either way.

Originally Posted by esldude

By out of phase I didn't mean necessarily inverse phase, just not lined up in phase with each other. Could have been 1 degree out or 5 degrees or whatever including 180 out. But yes that part of the math is quite simple.

Don't know what you are imagining that you are imagining either...

Quote:
Originally Posted by RazorJack

What parts in the video do you disagree with?

And how is any of the above relevant to 44.1 kHz as Nyquist frequency being adequate for (human... sorry dogs!) audio applications?

sorry but this argument is not worth my time...

Quote:

Originally Posted by Digitalchkn

Can we elaborate on the term "quality equipment"? I hope there is an understanding that the dynamic range of waveforms shown on analog scopes is nowhere near that of even 16 bits.

There is no doubt in my mind the video is a great introduction into the subject. There are other details at play that requires more in-depth look. Hence, professors in IEEE.

Quote:

Originally Posted by esldude

We could.  I have pointed to the video, they describe exactly what they are using.  So do I need to explain, describe, digest the details and spell them out for you or can you just watch it?  I take it by your comments you have not watched it.  Comments about the video make more sense when you have seen it.

I used to work for a well known scope manufacturer. I use higher end versions of this equipment on a regular basis for a living.  Are you still certain you'd like to get into the details of it?

As I said before, this is a good introductory material intended for noobs on the topic. For those who have studies this topic academically and/or work in related fields, this video has nothing to offer and in fact does not paint the full picture. Acceptance of this as gospel simply indicates illiteracy on the subject.  For more thorough introductory material at an academic level I highly recommend "Discrete-Time Signal Processing" by A. Oppenheim and R. Schafer 3rd edition, in particular Ch 1,2,4.  Please review that book prior to posting any arguments about sampling theory and DSP in general on this forum. Until then I have little interest in spending my time reviewing what is already well established knowledge.

Edited by Digitalchkn - 6/11/14 at 10:49am
Quote:
Originally Posted by groovyd

sorry but this argument is not worth my time...

Are we just supposed to assume that just because super audible frequencies exist, we need to make sure our stereo systems are capable of reproducing them? Just because computers and hard drives are cheaper and bigger than they used to be, should we allot massive amounts of bandwidth and processing power to things we can't even hear? That makes no sense whatsoever.

Quote:
Originally Posted by Digitalchkn

For more thorough introductory material at an academic level I highly recommend "Discrete-Time Signal Processing" by A. Oppenheim and R. Schafer 3rd edition, in particular Ch 1,2,4.  Please review that book prior to posting any arguments about sampling theory and DSP in general on this forum.

Ha! In order to use the English language effectively to communicate, I recommend reading all of Shakespere's works. Please read all of the plays and commit the sonnets to memory prior to posting anything on this forum.

Edited by bigshot - 6/11/14 at 11:06am
Quote:
Originally Posted by bigshot

Ha! In order to use the English language effectively to communicate, I recommend reading all of Shakespere's works. Please read all of the plays and commit the sonnets to memory prior to posting anything on this forum.

That's not right. I only recommended a few chapters not the whole thing.  Besides, I talk to you in prose and you talk back to me in slang. Some conversation!

Edited by Digitalchkn - 6/11/14 at 11:13am

Quote:
Originally Posted by bigshot

Is that Kirk Hammett? Of Metallica?

Quote:
Originally Posted by groovyd

sorry but this argument is not worth my time...

Your previous explanations are confusing and unclear what exactly you are talking about, especially when you don't include any graphics to illustrate the point you are trying to make, nor do you link or cite any sources where folks can go for a more in-depth understanding.

If I understand correctly, the issue at hand is regarding discrete-time sampling rates and the reconstruction of band-limited signals (and finite energy---like all real signals). In this case, in the xiph.org video, monty (correctly) explains how a real band limited signal is mathematically perfectly defined by sampling above the signal's nyquist frequency. In other words, given a set of discrete samples, there is exactly one and only one band-limited signal which perfectly intersects all of the sample points. This concept was clearly illustrated in monty's video. He further clarifies the point by demonstrating how the phase of the signal is perfectly captured by discrete time sampling. Again, this is the case because there is a one-to-one relationship between a discrete-time sampled waveform and its corresponding band-limited continuous waveform.

You need to define what you mean by "near sine waves" and relate the difference between a actual sine wave and whatever this other thing is that you are talking about, and then relate what additional Fourier coefficients your near sine waves have in addition to the fundamental. Then you need to relate how those harmonics relate to the concept of a band-limited signal. If you've added Fourier components that exceed one half of the sampling frequency, you have violated the Nyquist criterion and you are now discussing a different topic than covered in the video.

The logical flow of the arguments is:

1) there is a reasonably well defined frequency range of human hearing ( e.g., 20Hz -- 20kHz ). There may be exceptions, but by a few % of the Hz one way or another, and certainly not by a factor of 2 in either direction.

2) neither subsonic nor ultrasonic frequencies contribute to the audibility of sounds (this is by definition, "subsonic" meaning lower than what can be heard, etc.)

the corollary here is that all sound that can be heard fits neatly into the band-limited frequency range defined by human hearing (e.g., 20Hz--20kHz).

3) discrete-time sampled sound at frequencies of 44.1kHz or more is sufficient to mathematically define all the energy in a signal band-limited in the human audible range. [1]

Therefore, sampling above twice the highest frequency in the band-limited signal is mathematically sufficient to fully define the continuous time waveform.

If the wikipedia source is wrong, I encourage you to use your master's degree-level knowledge on the topic to corrected or amend the article. However, in this case, I don't anticipate that you will overturn the fundamental concept of the Nyquist-Shannon sampling theorem. Perhaps others can chime in with sources of the other bullet points on the list as I am quite busy at work now. Maybe I can fill it in later if there is interest, but the sources are already linked in other parts of the forum, so you can use your googlefu to find it.

Cheers

Quote:
Originally Posted by ab initio

If I understand correctly, the issue at hand is regarding discrete-time sampling rates and the reconstruction of band-limited signals (and finite energy---like all real signals).

Cheers

It's been a little while for me so my math may be a bit rusty and I may need some help with this.  If we let x(t)=sin(2π ft), which is a real signal and plug it into the definition for finite total energy of a signal, which is given by:

That doesn't look like E < inf. Anything I am missing?

Edited by Digitalchkn - 6/11/14 at 12:30pm
Quote:
Originally Posted by Digitalchkn

It's been a little while for me so my math may be a bit rusty and I may need some help with this.  If we let x(t)=sin(2π ft), which is a real signal and plug it into the definition for finite total energy of a signal, which is given by:

That doesn't look like E < inf. Anything I am missing?

It's also been a while for me, but something like a sinusoid over infinite time does have infinite energy. (Think of a voltage signal like that operating for eternity—you'd need an infinite amount of energy from some source to keep applying that voltage across a resistor or something.) That's why these are analyzed in terms of power, so divide by the time of integration. If you're not integrating over infinite time and you're not integrating something that's going to infinity in nasty ways, then the integral will be finite.

Look at power spectral density, etc. and see if there is nonzero content at frequencies above Nyquist. Or just filter those frequencies out, depending on the application.

Actually, I'm not quite sure if I followed the motivation for the question, but I haven't really been following the thread.

Quote:
Originally Posted by Digitalchkn

It's been a little while for me so my math may be a bit rusty and I may need some help with this.  If we let x(t)=sin(2π ft), which is a real signal and plug it into the definition for finite total energy of a signal, which is given by:

That doesn't look like E < inf. Anything I am missing?

Well, either a) the signal must be finite in length, (i.e., at some point for t < t_0, x(t)==0 and for t > t_end, x(t) ==0). Here's a link to a university lecture that discusses energy in signals (http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/5_10node10.html). Here they require a finite length signal.

Or b) you can talk about the signal's energy per unit time. I believe this is the more typical case. Here, Parseval's theorem is useful for showing that the energy in the signal is the same whether you calculate it in time domain or Fourier domain (http://en.wikipedia.org/wiki/Parseval%27s_theorem). One might do this by considering the energy of some periodic signal. One integrates over the period of the signal.

The energy in the signal is bounded if the energy in the Fourier coefficients decrease sufficiently fast with increasing wavenumber. In the case of a band-limited signal, this is the case, because all Fourier coefficients are zero beyond the Nyquist frequency.

Cheers

Quote:
Originally Posted by Digitalchkn

Quote:

Quote:

I used to work for a well known scope manufacturer. I use higher end versions of this equipment on a regular basis for a living.  Are you still certain you'd like to get into the details of it?

As I said before, this is a good introductory material intended for noobs on the topic. For those who have studies this topic academically and/or work in related fields, this video has nothing to offer and in fact does not paint the full picture. Acceptance of this as gospel simply indicates illiteracy on the subject.  For more thorough introductory material at an academic level I highly recommend "Discrete-Time Signal Processing" by A. Oppenheim and R. Schafer 3rd edition, in particular Ch 1,2,4.  Please review that book prior to posting any arguments about sampling theory and DSP in general on this forum. Until then I have little interest in spending my time reviewing what is already well established knowledge.

Yes, I suppose we can get into if you like. You asked what I meant by "quality equipment".  The equipment is clearly specified in the video.  If you have the idea we are acting as if we can discern 16 bit precision on a scope, well, neither I nor the video made any such claim.  By quality I meant an analog based source for highly precise, very low distortion test signals and analog based, highly precise, very low distortion spectrum analyzers.  Things that were obvious on a scope are things like the idea you don't get good clean sine waves out of AD/DA conversion using only slightly more than 2 samples per wave.  You do.  You couldn't specify it was .05% distortion looking at the scope.  Combine it with a spectrum analyzer and you can see there no large levels of distortion either.  Straightforward stuff indeed.

The premise of the video is if you don't know or don't believe digital can do what it claims as cleanly as it claims you can investigate with good analog equipment what it can and what it cannot do.  The analog results show that up to 20khz digital is as clean and accurate as it claims to be.  Of course any such introductory type video isn't in depth or detail for any tiny issue one may have with digital audio.  But one could do the same thing if they wished and investigate whichever issue they think they are having.

So with your advanced knowledge and literacy in things digital what are the problems of digital processing in audio?

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