24/192 music downloads are useless??

[mtrycrafts]

Remember I'm only talking about digital reconstruction, not about what can actually be heard by human ears. When sampling an input signal with the frequency at half the sampling rate the best achieved would be a triangle wave (samples taken at peaks) and the worst would be no waveform (samples taken at zero crossing), this depends on how your sample clock matched up with the incoming signal. Now as the input signal frequency decreases you are guaranteed to have one of the two points being non-zero and the frequency component is therefore retained. Now all input frequencies from the sampling rate / 2 (22050) to sampling rate / 3 (14700) will be represented by only two points placed "somewhere" on the slopes of the sine wave. So my question here is will those two digital points provide an accurate representation of the amplitude of that input sine wave?

Steve

All one has to do is input a 20kHz sive wave from a source and look at the input and output from that player, or DAC, whatever, and you will see it is reproduced accurately.
Without it, digital audio would just not work.
That graph is inadequate to tell us anything. Where was it taken in the chain?
Who is claiming the necessity for 4x sampling of the higher frequencies?

 

[mtrycrafts]

Now my answer to that would be no, I really don't see how you could consistantly capture the actual amplitude with only two points per cycle. In my mind you'd see the frequency with a varied amplitude as the two points move along the sine wave on each following cycle.

Going back to my previous statement, if I now have 4 samples per cycle on the sine wave I'd end up with a pretty good approximation of the amplitude regardless of their position on the sine wave.

So no hidden questions, it just looks to me like the representation of input frequencies from the sampling rate / 2 down to sampling rate / 4 will be far from a good approximation. So is my thinking process off here?

Steve

P.S. Gotta take the dog to the park now but maybe there is an easy way to prove/disprove this? How about testing with a lower sampling rate (4 kHz) and an input sine wave signal with a frequency that falls more into our normal hearing range (1000-2000Hz).

Here is another link to a different wiki page:
Nyquist

In essence, the theorem shows that a bandlimited analog signal can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency of the original signal.

This might also help altyhough I didn't watch the program from MIT:
http://academicearth.org/lectures/nyquist-theory-pam-qam-and-frequency-translation

 

[avnetguy]

The source of those graphs is me. I used Audacity to mathematically generate the sine wave tones and they showed exactly what I had expected.

Steve

 

[mtrycrafts]

The source of those graphs is me. I used Audacity to mathematically generate the sine wave tones and they showed exactly what I had expected.

Steve

Don't know how it works but
Most likely it is not what would be reconstructed and the output of a DAC. It has to output the input signal, period.

There are a number of very smart folks at AVS that could show you and explain where the error is in your graphs.

 

[avnetguy]

Here is a follow up from the previous graphs but a real world example with a screen capture showing three waveforms.

The bottom graph shows a 16bit 44.1kHz generated 3900 Hz sine wave and this is the source file I played back via Winamp. The top and middle graphs are the recordings made via the onboard soundcard at 16kHz and 8kHz respectively. While we can't compare actual levels between the source and the two recordings as these are affected by the input/output mixer levels we can compare the two recorded waveforms as nothing was adjusted between the two recordings other than the sample rate.

So based on these examples do we believe that waveforms with frequencies up to the sampling rate / 2 (minus 1 or less) are accurately represented? And just to state again, I'm not trying to evaluate whether or not the differences can be heard, that's a different test, just that the digital representation seems to fall short in the stated situation.

Steve

 

[avnetguy]

Don't know how it works but
Most likely it is not what would be reconstructed and the output of a DAC. It has to output the input signal, period.

There are a number of very smart folks at AVS that could show you and explain where the error is in your graphs.

If you know any of these AVS folks, please invite them over as I'd like to understand it.

Steve

 

[cpp]

Man this thread reminds me of work ( retired Bell Labs and Lucent engineer)

 

[MDS]

Here is a follow up from the previous graphs but a real world example with a screen capture showing three waveforms.

The bottom graph shows a 16bit 44.1kHz generated 3900 Hz sine wave and this is the source file I played back via Winamp.

Can you explain what you mean by that? It can't be both 16 bit 44.1 kHz AND 3900 Hz if it is a pure sine wave. The bit depth Audacity uses internally is likely 32 bit float. Note that Audacity didn't 'sample' anything to create the waveform.

I can generate a 3900 Hz sine wave with Sound Forge and if you zoom out it looks like a smooth sine wave, not the jagged mess your graph shows.

 

[avnetguy]

Man this thread reminds me of work ( retired Bell Labs and Lucent engineer)

lol, yes it is too much like work, in fact digital audio is my daily work and has been for the past 17 years.

Steve

 

[avnetguy]

Can you explain what you mean by that? It can't be both 16 bit 44.1 kHz AND 3900 Hz if it is a pure sine wave. The bit depth Audacity uses internally is likely 32 bit float. Note that Audacity didn't 'sample' anything to create the waveform.

I can generate a 3900 Hz sine wave with Sound Forge and if you zoom out it looks like a smooth sine wave, not the jagged mess your graph shows.

Just a quick response as I'm at work right now.

The sampling rate in Audacity is set to 44.1 Khz using 16 bit data (not the default floating point values, don't use these) and 3900 Hz is frequency of the tone generated. And yes, the original 3900 Hz tone is generated as I don't have my sine wave generator handy but it'll end up being the same thing anyways.

I can go into more detail later on tonight if you like.

Steve

 

[Josuah]

So here is a quick visual example that shows the difference in the actual amplitude captured.

Both sides show sine waves (top to bottom) at 3900, 3500, 3000, 2500 Hz.
The left side is sampled at 16000 and the right side 8000.

So visually it is pretty obvious at the sample rate of 8000 the amplitude of the signal is not represented very well as your input signal approaches 4000.

Steve

Your plots are using straight lines for connecting the points. I can't recall the exact information, but when reconstructing the original waveform you are not supposed to use straight lines between the sample points.

 

[PENG]

Just a quick response as I'm at work right now.

The sampling rate in Audacity is set to 44.1 Khz using 16 bit data (not the default floating point values, don't use these) and 3900 Hz is frequency of the tone generated. And yes, the original 3900 Hz tone is generated as I don't have my sine wave generator handy but it'll end up being the same thing anyways.

I can go into more detail later on tonight if you like.

Steve

Steve, are we now just talking about practical limitations in implementation? Or you still do not believe two non zero points of a sine wave within one cycle will allow us to reconstruct the wave accurately in theory?

 

[avnetguy]

Can you explain what you mean by that? It can't be both 16 bit 44.1 kHz AND 3900 Hz if it is a pure sine wave. The bit depth Audacity uses internally is likely 32 bit float. Note that Audacity didn't 'sample' anything to create the waveform.

I can generate a 3900 Hz sine wave with Sound Forge and if you zoom out it looks like a smooth sine wave, not the jagged mess your graph shows.

Now that I'm home I'll see if I can explain it in better detail.

Using that last image I posted (plot of three waveforms), lets focus on the bottom one. That plot represents what a 44100 Hz recording using 16 bit resolution (same as regular CD audio) of a 3900 Hz input sine wave signal. Now given our sampling rate is 44100 Hz that means the A/D will output one 16 bit value (a sample) every 22.6 microseconds. Next we have a 3900 Hz sine wave which means we have one complete cycle every 256 microseconds. So when the computer records this sine wave it is represented by (256 / 22.6) 11 samples. These 11 samples are all that is stored and later used to recreate the one cycle of the 3900Hz signal on playback.

To answer your question, the "jagged mess" is exactly what the computer (or CD playout device) sees when it is read out from the file or disc and heads for the D/A converter. So if your computer program is displaying more than the 11 samples per cycle then it is mathematically filling in the sine wave as you zoom in and that does not represent what is equal to the data a CD audio file would have.

Does that help?

Steve

 

[avnetguy]

Steve, are we now just talking about practical limitations in implementation?

If I understand your question correctly, yes we would be discussing the practical limitations of CD quality digital data.

Or you still do not believe two non zero points of a sine wave within one cycle will allow us to reconstruct the wave accurately in theory?

From a pure digital analysis perspective CD quality definitely seems to fall short, that of course assuming an accurate reproduction (+/- 0.5 db?) of 20Hz - 20kHz would be the target.

In real world listening terms ... well, I can't hear (or at least differentiate) much above 13 or 14kHz anyways so CD quality is fine by me. Of course others with better hearing than I might disagree.

Steve

 

[mtrycrafts]

..
To answer your question, the "jagged mess" is exactly what the computer (or CD playout device) sees when it is read out from the file or disc and heads for the D/A converter. ...

Does that help?

Steve

Perhaps then, you are looking at the wrong place to see if the D/a will correctly reproduce those samples. It seems you are looking at it before the D/A. You need to look at the analog output and compare it to the original analog input. You seem to be worrying what it looks like inside the samples and before the actual reconstruction, the analog out? That is why it doesn't look like a sine wave but connected dots of the samples?

 

[avnetguy]

Perhaps then, you are looking at the wrong place to see if the D/a will correctly reproduce those samples. It seems you are looking at it before the D/A. You need to look at the analog output and compare it to the original analog input. You seem to be worrying what it looks like inside the samples and before the actual reconstruction, the analog out? That is why it doesn't look like a sine wave but connected dots of the samples?

One step at a time, we'll be getting to that ....

Hey, I just saw this thread and it got me "thinking out loud" (read: posting quick thoughts). I might very well be a "few fries short of a happy meal here".

But seriously, maybe there is some interpolation or analog "magic" going on, I just don't see it .... yet. Like I mentioned before, if I had a DSO (and other calibrated equipment) we could just jump to the end game but I don't.

Steve

 

[mtrycrafts]

One step at a time, we'll be getting to that ....

Hey, I just saw this thread and it got me "thinking out loud" (read: posting quick thoughts). I might very well be a "few fries short of a happy meal here".

But seriously, maybe there is some interpolation or analog "magic" going on, I just don't see it .... yet. Like I mentioned before, if I had a DSO (and other calibrated equipment) we could just jump to the end game but I don't.

Steve

You may, or not, want to read some of this thread:
24/192 Music Downloads and why they make no sense - Page 5 - AVS Forum

 

[PENG]

If I understand your question correctly, yes we would be discussing the practical limitations of CD quality digital data.


From a pure digital analysis perspective CD quality definitely seems to fall short, that of course assuming an accurate reproduction (+/- 0.5 db?) of 20Hz - 20kHz would be the target.

In real world listening terms ... well, I can't hear (or at least differentiate) much above 13 or 14kHz anyways so CD quality is fine by me. Of course others with better hearing than I might disagree.

Steve

Thank you for clarifying your position on this. On the implementation side I do not know enough to contribute to any further discussion despite my interests in the topic. On the thoretical side, those links provided by others so far do indicate/explain how 44.1kHz is high enough to reconstruct a bandlimited signal perfectly. Just to save those interested in reading up going back a couple of pages, here are two wiki links (wish I could but can't link to text books)

Nyquist

http://en.wikipedia.org/wiki/Sampling_(signal_processing)

To understand the contents, some background in basic telecommunications and electrical theory as well as calculus, infinite series, Fourier transform, Nyquist among others, would certainly help.

 

[PENG]

You may, or not, want to read some of this thread:
24/192 Music Downloads and why they make no sense - Page 5 - AVS Forum

Could you point us to the post so we don't have to read the whole thread?

 

[PENG]

One step at a time, we'll be getting to that ....

But seriously, maybe there is some interpolation or analog "magic" going on,

Steve

may be? To me it is a given, you can't reconstruct the original analog signal form pulses without some interpolation. The point is, such interpolation should get you the original signal perfectly, and yes it can, unless the original signal has discontinuities such as a square wave, but we are talking about music waveforms here, that are composed of fundamentals and harmonics, all sine waves individually though we all know they don't look like sine waves collectively.