Understanding Sample Rate

[kumakuma]

1 hour ago, beerandmusic said:

 

even man can create sound at an "infinite rate"...the plucking of a guitar for instance.

the complex waveform has an infinite number of frequencies, at an infinite number of time slices,  within it's own frequency range (between 50 and 300hz) that man just is not able to record accurately.

 

rate is the same thing as frequency

 

waveforms do not have an infinite number of frequencies, they have one frequency at any arbitrary point in time

 

[tmtomh]

2 hours ago, kumakuma said:

 

Averaging is the wrong way to think about it. The two sound waves combine to make one sound wave.

 

Perhaps this video would help:

 

 

 

Thanks for this! If "digital sampling is just slices of music with gaps in between" is the #1 myth about digital, then this issue - "complex signals are fundamentally different than simple signals when it comes to the ability of digital sampling to record them" - has got to be the #2 myth. This, I think, really explains and shows the reality clearly for those who don't agree or understand.

[mansr]

19 minutes ago, kumakuma said:

waveforms do not have an infinite number of frequencies, they have one frequency at any arbitrary point in time

Wrong. Frequencies don't exist at points in time. Waveforms have a set of frequencies (possibly only one) over an interval of time.

[kumakuma]

Just now, mansr said:

Wrong. Frequencies don't exist at points in time. Waveforms have a set of frequencies (possibly only one) over an interval of time.

 

I was trying to make it easier for our dear friend here to imagine a waveform. I'll return to just making snide comments.  

[mansr]

45 minutes ago, jabbr said:

Hmmm ... it’s often though that SDM is less intuitive than PCM

It is. SDM is based on sampling, just like PCM, and then adds heaps of additional maths on top. If you don't understand sampling according to Shannon-Nyquist, you don't have a chance of understanding SDM.

 

45 minutes ago, jabbr said:

but it’s also described as “analog”

That is fundamentally wrong.

[crenca]

14 minutes ago, mansr said:

Wrong. Frequencies don't exist at points in time. Waveforms have a set of frequencies (possibly only one) over an interval of time.

 

A dirac pulse is (or does it merely approach?) a state of energy at a "point in time" (or is this incorrect?), but by definition a frequency assumes a period of time...

[Don Hills]

5 hours ago, mansr said:

That's a gross over-simplification but more accurate than the previously offered "explanation."

 

  Just setting the level of "simplification" at the level of the intended recipient.

My daughter is just starting the 3rd year of an Astronomy degree. In her first physics lecture yesterday, they began by saying "Everything we've taught you in the last two years was simplified. Now we're going to teach you how it really works."

[mansr]

17 minutes ago, crenca said:

A dirac pulse is (or does it merely approach?) a state of energy at a "point in time" (or is this incorrect?), but by definition a frequency assumes a period of time...

A Dirac pulse is a signal whose value is non-zero at one single instant and zero for infinite duration before and after. It contains all frequencies from zero to infinity throughout the infinitely long interval.

[Don Hills]

3 hours ago, beerandmusic said:

 

i changed my name the moment that you did not sample....i changed it back the next moment you did not sample....you have the correct current name but you have no knowledge of the moment i changed my name....you are missing the details....but it doesn't matter now, because it is in the past.

 

This is incorrect. The moment that you changed your name in between samples was accurately recorded. Monty's video shows this happening - starting at about the 17 minute mark, he shows what happens when an event (the transition of a square wave) is moved between sampling instants. 

 

Edit: I think I misunderstood your example. You changed your name, then changed it back again, in between 2 samples. By definition, this equates to a frequency greater then half of the sampling rate. Nevertheless, if the name was different for a finite amount of time, some part of your name change was captured. Again, Monty shows this in the video.

 

Edit 2: No, on third reading, I think I understood you correctly the first time. I'll leave the second explanation for completeness. 

[Don Hills]

1 hour ago, beerandmusic said:

P.S. Thanks for spending so much time patiently with me. ....

 

For me at least, I'm not doing this just for you. Your misunderstandings are quite commonly held, and I'm sure there are many silent followers of this thread labouring under the same misunderstandings.

[Don Hills]

2 hours ago, beerandmusic said:

...

the complex waveform has an infinite number of frequencies, at an infinite number of time slices,  within it's own frequency range (between 50 and 300hz) that man just is not able to record accurately.

 

Nevertheless, provided those frequencies are all less than half of the sampling rate, they can be accurately sampled and reproduced.

[crenca]

10 minutes ago, mansr said:

A Dirac pulse is a signal whose value is non-zero at one single instant and zero for infinite duration before and after. It contains all frequencies from zero to infinity throughout the infinitely long interval.

 

Ah, a pulse of the gods then...

[adamdea]

17 minutes ago, mansr said:

A Dirac pulse is a signal whose value is non-zero at one single instant and zero for infinite duration before and after. It contains all frequencies from zero to infinity throughout the infinitely long interval.

This is I think why Fokus reminded me that when you apply a Dirac to a linear phase filter, the ringing is caused by what the filter takes away, not what it adds. 

[jabbr]

2 hours ago, beerandmusic said:

 

even man can create sound at an "infinite rate"...the plucking of a guitar for instance.

 

???

 

2 hours ago, beerandmusic said:

the complex waveform has an infinite number of frequencies, at an infinite number of time slices,  within it's own frequency range (between 50 and 300hz) that man just is not able to record accurately.

 

Aside from whether a truly infinite number of frequencies can exist — as I’ve said above they physically can’t — you should perform an exercise to demonstrate to yourself how close frequencies affect a common waveform:

 

Take an 8hz and a 10hz sine wave over a few seconds and additively combine the waves and plot. What do you see?

 

Take two 8hz waves having different phases and additively combine. What do you see?

[mansr]

8 minutes ago, jabbr said:

Aside from whether a truly infinite number of frequencies can exist — as I’ve said above they physically can’t —

Whether an infinite number of frequencies can exist isn't important in practice. What matters is that they can't be infinitely high.

[tmtomh]

5 hours ago, beerandmusic said:

 

i changed my name the moment that you did not sample....i changed it back the next moment you did not sample....you have the correct current name but you have no knowledge of the moment i changed my name....you are missing the details....but it doesn't matter now, because it is in the past.

 

Apologies in advance for repeating the concept others have tried to explain above, but in the hopes of getting through to you I'll add my attempt.

 

Here's what you are proposing:

 

Step 1. Your name is A

Step 2. Digital system samples your name and it's A.

Step 3. You quickly change your name to B

Step 4. You quickly change your name back to A

Step 5. Digital system samples your name again, and it's A.

 

In this scenario, the actual course of events is A-B-A, but the digital sampler only encodes A-A. Therefore, in your scenario, the digitally sampled music misses the zig-zag to and from B, and plays back only A-A, therefore losing the fine detail of what actually happened.

 

Your example is indeed applicable to the world of digital sampling - but it is not applicable in the way you have been insisting.

 

A sound wave that changes and then changes back again too fast for a digital sampling system is not "extra fast" music or "really detailed" music. It is a higher frequency than the sample rate can capture. This is why I and others have been telling you over and over that sample rate is not about how fast the sampler can record the music, but rather about how high of a frequency the sampler can encode.

 

It's also why I wrote to you in an earlier comment in this thread that there simply never is any "extra detail" in between samples, except if the sound is at a higher frequency than the digital sampling system can encode (if it's above the Nyquist limit of 1/2 the sample rate).

 

Remember the example of how a 44.1k sampler cannot distinguish between 15kHz and 30kHz? 15kHz is, in your example, A-A, while 30kHz is A-B-A: 30kHz has that extra "zig zag," an extra oscillation cycle because it oscillates at the double the frequency (speed) of 15kHz. So a 44.1k sampler will not miss "detail" in a musical signal that happens to contain 30kHz information (which is above our hearing range). No, it simply will mistakenly encode 30kHz as 15kHz unless you filter the incoming signal to remove all frequencies above 22.05kHz (the Nyquist limit for a 44.1k sampling system), which is what digital music systems do. But for all the sound up to 22.05kHz, a 44.1kHz sampling system will encode the values just as accurately as a 192k sampling system.

 

The reason the Nyquist limit is 1/2 the frequency of the sample rate is that the sampler needs to sample each frequency at least twice to enode it accurately. I know it might sound bonkers to you that digital sampling can accurately reconstruct a sound wave by sampling it only twice, but there it is.

[fas42]

7 hours ago, beerandmusic said:

 

agree, this is more along my interests, and probably instead of starting a thread "understanding sample rate", in hind sight, i should have started a topic "why does sacd sound better than a cd for the layman". (wink)

 

What a lot of people in audio don't appreciate, even though they will always pay lip service to it, is that the quality of the implementation, how well the real world stuff does its job, is far, far more important to the subjective takeaway, than the "exciting" technology being used; the latter is the sort of thing that gets geeks in a lather, and produces brilliant numbers - but ultimately may not satisfy, long term, because some key things, which are not being measured, are not being done well enough.

 

SACD will sound better, for some people, than CD because the particular set of components happen to get some aspects of the reproduction "sounding better" - because the combo of design, parts, construction just happens, largely by accident, to do a better job of producing satisfying sound for those people. Men tend to be obsessed with stuff that produces impressive numbers, rather than a package that is balanced and "does everything well enough" - in audio, the latter is very, very important, and if not taken into account will result in a somewhat disappointing end point.

 

So, it's not the technology that matters - it's how well the bits of real world materials are put together to make it all work that dictate whether it gets a thumbs up, or down.

[fas42]

Since the misunderstanding is partly the "joining the dots" aspect, just consider that the dots to be firstly, totally accurate in the value they are; that is, the sampling was done as well as conversion circuits could do such a job. Then, the reconstruction is merely to join those dots - and theoretically there are an infinite number of ways that any two adjacent dots could be joined; any sort of funny squiggle could be drawn between the two - and, the dots are joined! But, there is a problem - if a funny squggle is used then then you have incorporated frequencies which are not allowable - above the audio band, in the case of CD; and, a straight line is just as bad, the sharp points you now see at all the dots are not allowable either; they are effectively very high frequency glitches, not audio stuff!

 

It turns out there is one, and one only, smoothly curving line that can join the dots, any two dots, which stops frequencies which are not allowable being incorporated in the final waveform - that's how the circuit "knows" it's getting the reconstruction right; no "wrong" frequencies are in the end product. In the real world, a filter is what does this job, forcing the waveform to always exclude "wrong" frequencies.

[Ralf11]

17 hours ago, Spacehound said:

You're like a sponge. Absorbs anything. But real sponges have got an organ that expels crap.

 

nuh unh - no organs in sponges

[Ralf11]

12 hours ago, pkane2001 said:

 

I can't believe we are still arguing about a mathematical concept proven nearly a century ago. Just like Beer, you are wrong if you are talking about a periodic signal. Sampling over the Nyquist rate does nothing to improve the accuracy of the reproduction.

 

 

you have never taught Evolutionary Biology, have you?

[jabbr]

4 hours ago, mansr said:

Whether an infinite number of frequencies can exist isn't important in practice. What matters is that they can't be infinitely high.

 

Whether a frequency can be infinitely high is neither important in practice because you can't detect it. 

 

The uncertainty principle places a limit on the ability to resolve closely space frequencies and SNR.

 

In any case the range of frequencies is similar to the range of velocities. Both have instantaneous values when used to describe objects. Both are real numbers whose measured values are described/bounded by physics.

[esldude]

8 minutes ago, jabbr said:

 

Whether a frequency can be infinitely high is neither important in practice because you can't detect it. 

 

The uncertainty principle places a limit on the ability to resolve closely space frequencies and SNR.

 

In any case the range of frequencies is similar to the range of velocities. Both have instantaneous values when used to describe objects. Both are real numbers whose measured values are described/bounded by physics.

Let us keep it simple till the concepts are clear to those who don't know them.  We can fill in the real world limits and messiness later. 

[beerandmusic]

8 hours ago, kumakuma said:

 

waveforms do not have an infinite number of frequencies, they have one frequency at any arbitrary point in time

 

 

 

7 hours ago, mansr said:

Wrong. Frequencies don't exist at points in time. Waveforms have a set of frequencies (possibly only one) over an interval of time.

 

if frequencies don't exist at a point in time, what is being measured at sample time?

it may not be a frequency that can be output without time, but it is plotting a point of of the composite frequencies in the complex signal?

 

 

 

[kumakuma]

2 minutes ago, beerandmusic said:

does a complex waveform not have multiple frequencies?  I believe we can hear more than one frequency at any one time.

 

Did you watch the video I recommended about how complex waveforms are created from simple waveforms?

[beerandmusic]

3 minutes ago, kumakuma said:

 

Did you watch the video I recommended about how complex waveforms are created from simple waveforms?

I watched about 1 minute of it and was very interesed....i was planning on finishing watching that when i first got up....i should have before starting to read and respond (wink)...will go watch it now, before reading more....