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Thread: Here’s A Digital Conundrum

  1. #1
    Join Date: Aug 2008

    Location: Suffolk, UK

    Posts: 1,218
    I'm Paul.

    Default Here’s A Digital Conundrum

    If you have an analogue waveform, ie. music, and at roughly every 0.023 microseconds (44,100 times per second) you measure the amplitude of the waveform and assign it to the closest level out of the 16,536 descrete steps that you have available how much as a percentage of the waveform have you actually measured?

    Basically this is Redbook standard analogue to digital conversion. It sounds like 44,100 times a second and 65,536 steps in voltage (for 2 volts output thats steps of around 0.03 microvolts) is quite a lot, but when you try to equate that to exactly how much as a percentage of the original waveform you have measured you can’t, can you?

    What if we now take the measurement every 192,000 times a second and increase the number of steps to 16,777,216 (192Khz, 24 Bit) we take a lot more measurements but again try to equate this to a percentage of the original waveform I can’t seem to do it?

    It seems no matter how many times you take a measurement the vast majority of the orginal waveform disregarded.

    This has baffled me.. Anyone?
    ~Paul~

  2. #2
    Join Date: Jan 2008

    Location: Forest of Dean, Glos

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    I'm Jerry.

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    In terms of sampling rate you have captured ALL of it, literally all of it, for frequencies below half your sampling rate, 22KHz in the case of Red Book.
    The dynamic quantisation I'm not sure about.
    Jerry

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  3. #3
    Join Date: Mar 2009

    Location: South West-ish, UK

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    I'm Patrick.

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    It's a meaningless conundrum; if you sample an analogue waveform that is band-limited to less than half the sampling frequency, then you have captured 100% of the information present.

    Analogies are always questionable, but think of a bag full of coins: if you squeeze all the air out of the bag, how much money have you lost from your bag?

  4. #4
    Join Date: Aug 2008

    Location: Suffolk, UK

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    I'm Paul.

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    I’m not so sure that you have captured all of the waveform for frequencies below half of the sampling rate. I don’t see it as a meaningless conundrum either, as it eludes to the fact that you are not recording a significant part of the waveform.

    Draw a rough, squiggly horizontal line across a page and pick a few points and then measure the height of these points from the bottom of the page to the nearest millimetre. How much of that line have you actually recorded? Not a lot. Your measurements are of instance points that have no horizontal width. Your line has a definite horizontal width. Okay, you can take more measurements but they remain just measurements of instances that cannot describe what is happening between each measurement point.
    ~Paul~

  5. #5
    Join Date: Jan 2008

    Location: Forest of Dean, Glos

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    I'm Jerry.

    Default

    Quote Originally Posted by Primalsea View Post
    I’m not so sure that you have captured all of the waveform for frequencies below half of the sampling rate.
    It's not a matter of debate, actually - it's mathematically rigorous. It's the way our universe works. Check out Nyquist theorem.

    You'd need to find a wormhole in space-time to enter a universe with suitably different physical laws than ours in order for it not to be the case.

    Start here, maybe -- https://en.wikipedia.org/wiki/Sampli...Audio_sampling
    Jerry

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  6. #6
    Join Date: Mar 2010

    Location: Sheffield

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    I'm Simon.

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    The Nyquist/Shannon sampling theorem is proven. End of story, it's mathematically perfect. That of course doesn't mean that its implementation in silicon and volts back here in the real world is perfect. Signals need reconstructing (with limited tap length filters), levels need quantising (with limited voltage levels) timing needs to be recovered (with jitter imperfect clocks and transmission). There's a whole host of reasons why the function might not perfectly follow the theory.

    Of course there's bugger all good science to prove which of these are audible.
    Kuzma Stabi/S 12", (LP12-bastard) DC motor and optical tacho psu, Benz LP, Paradise (phonostage). MB-Pro, Brooklyn dac and psu, Bruno Putzeys balanced pre, mod86p dual mono amps, Yamaha NS1000m

  7. #7
    Join Date: Aug 2008

    Location: Suffolk, UK

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    I'm Paul.

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    No one is saying that Nyquist or Shannon theorem is wrong, when did I say that?

    What I am saying is how can you just take it for granted that the information that existed between 2 sampling points was irreverent.
    ~Paul~

  8. #8
    Join Date: Aug 2009

    Location: Staffordshire, England

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    I'm Martin.

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    Quote Originally Posted by Primalsea View Post
    No one is saying that Nyquist or Shannon theorem is wrong, when did I say that?

    What I am saying is how can you just take it for granted that the information that existed between 2 sampling points was irreverent.
    Because it isn't really 'information', it's just a rise or a fall in voltage. There isn't really a 'gap between the samples' for anything to be missing from. Think about it that way.
    Martin



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  9. #9
    Join Date: Mar 2010

    Location: Sheffield

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    I'm Simon.

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    Paul, sampling theorem doesn't define the points in isolation, it defines the minimum number of points required to accurately reconstruct the signal curve that passes through any number of consecutive points. forget the dots, its the line that passes through them that were interested in and how accurately that mimics the originally sampled signal.
    Kuzma Stabi/S 12", (LP12-bastard) DC motor and optical tacho psu, Benz LP, Paradise (phonostage). MB-Pro, Brooklyn dac and psu, Bruno Putzeys balanced pre, mod86p dual mono amps, Yamaha NS1000m

  10. #10
    Join Date: Mar 2011

    Location: Readimg

    Posts: 83
    I'm George.

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    There are two parts to this problem. If you analyse a music signal you will find it is made up of a lot of frequencies. In fact, you can make up the music signal from a lot of sine waves of different frequencies and amplitudes. If you analyse the signal there will be sine waves at a whole range of frequencies, all at different amplitudes. However, if it is a music signal then there will less and less of the very high frequencies and there will be very little above 20 kHz. So if you then apply a filter to the signal so that nothing above 22 kHz can get through then there cannot be any sine waves above 22 kHz and it is assumed you have not lost any music.

    Right now let's digitise. If you wanted to sample a 30 Hz bass organ signal then you could sample at 60 Hz and assume the signal is a sine wave and you can reconstruct it. OK if there is a squiggle on it then that squiggle has to be a higher frequency but that is OK for us as in reality we are sampling at 44.1 kHz, so you can sample finer and finer squiggles all the way up 22 kHz. Ah, but what happens if there is a squiggle on top the 22 kHz frequency? There isn't any because you filtered everything above 22 kHz out.

    So music consists a lot of sine waves of different frequencies and amplitudes. If you filter it so nothing above 22kHz can get through then sampling at 44 kHz will reproduce the whole music signal as there can't be any smaller squiggles.

    Making that happen in practice is the tricky bit.

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