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Thread: Question of theory...

  1. #1
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    Question of theory...

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    When presented with a frequency responce range, I understand what's being referenced: 20-20,000Hz/Low to high frequency.
    But when I read about a sampling rate I'm lost. "44.1 kHz" or "96kHz" doesn't say anything to me. Can somebody explain? I've got Paul White's Basic Digital Recording but while it uses these terms, it doesn't really define them for me.

    Also, I know that dB is a unit of sound refering to volume, but again, when expressed as a "dynamic range" I don't get it. How can a unit with a negative component (-6dB for example) have a positive function. I would have thought that -6dB would be measurement of silence! Help me out!
    Cheeseburgers Rock!

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    Sampling audio is analogous to a movie film. A film is really a series of still-life snapshots played in succession. To capture motion with film, you need to take something like 25-30 snapshots per second. Sampling audio is the same thing as filming a movie except that instead of taking snapshots of light, you take snapshots of sound. And instead of taking 25-30 per second, you need to take around 44,100 per second if you want to capture the sound accurately. (44.1kHz = 44,100 snapshots/second) So the number you are seeing, 44.1kHz, is not a range but rather the rate at which snapshots (samples) are taken.

    In a film, if some motion were to happen very fast, say in less than 1/25th of a second, you might not have filmed it at all because the whole event occurred between two snapshots. The same thing happens in audio with high frequencies. The cycle of a high-frequency wave happens very fast. So if your sampling rate is not fast enough, you're going to miss it. For example, if you're trying to sample a 16kHz sound whose cycle occurs in 1/16,000th of a second, and if the sampling rate you're using is only10kHz (10,000 snapshots per second), you're not going to capture (record) that frequency. It will slip through the cracks. Sorry if all this sounded too simplified---I like the film analogy.

    I'll let the more knowledgeable recording engineers explain dB. But very quickly, the dB scale is relative to a specific sound level. So if your volume is less than that level, it will be expressed with negative numbers. If you're interested in reading, Electronic Musician magazine just had a two-part article explaining decibels. You can read it online here. Go to the July 2001 issue for part one.

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    First off, the word "frequency," by itself, means the same as "rate." Frequency of a simple sine wave means how many wave crests (the span from one wave crest to the next is one cycle) pass by in a given unit of time. The standard measurement is number of wave crests, that is, cycles, per second. The unit is named Hz (Hertz) after a scientist who did a lot of early work with waves (I forget his first name but it wasn't "Eddie"). For audio waves and electrical signals this is often in the thousands, hence a more useful unit is kHz (kiloHertz) -- so instead of always having to say "20,000 Hz" you can say "20 kHz."

    For sampling frequency, it's simply how many samples -- measurements of the waveform's amplitute at a given instant -- are made. So a sampling rate of 44,100 samples per second means that, in each second, the wave is measured 44,100 separate times.

    The other question is more complex and I'm not thoroughly sure of the details to really explain it well, but I'll take a crack at it. The measurements of sound pressure are expressed in a form that makes it easier for people who work with sound levels to deal with them. Instead of using a absolute value as the desired maximum level that you want to avoid surpassing, the max is set as zero. Values smaller than this are expressed as negative values and values above as positive values. So, to someone monitoring sound levels, positive values (to the right of 0) are bad -- the sound levels must be kept no higher than zero or the electronics in the recording/sound reproduction chain will be clipped. Not terribly unlike choosing the freezing point of water to be 0 degrees in the Centigrade system, and thereby expressing colder temperatures with negative values.

    Hope that helps. Maybe others can chime in and be more precise.

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    CD audio is 16 bits at 44,100K.Whatever your second # is in this format (divided by two) gives you the frequency responce in cycles per second.Therefor CD audio is good up to 22,050 cycles or Hz.Bit size relates to the resolution of the signal.
    So,why do you need more than 22,050 Hz?After all,human hearing cuts out about 20,000,right?
    The extra headroom (available space above the signal before it hits 0 dB) is the justification for 96K recording and extra resolution (bits) the justification for using 24 bits instead of 16.
    To make a CD,you still have to downsample back to 16 bit,44,100K audio,but the fidelity is noticeably better than if you had done the entire process at just 16 bit 44,100K.

    Tom


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    Wow! I guess Paul White's text assumes a certain level of basic knowledge. I in any case, thanks. Sample rate expresses how many times the signal is evaluated for reproduction. The more samples taken, the closer the signal can be matched acurately. 96kHz, while improbable to distiguish, affords a "buffer" that assures the greatest accuracy possible in a digital enviroment. The greater the bit rate, the more information exposed to sampling process. One doesn't provide a benefit without the other.

    The decible thing is still just a little elusive. I understand the "absolute zero" reference. But what establishes zero? Is that a universal fixed point? And math-wise, if somebody says "6 dB cut", we're dropping the minus symbol because 6dB is being expressed as an amount rather than a range. Right?

    Noticed a couple of you guys are from where I was raised in the Bay Area. Went to grade school thru junior college in Cupertino. Dad and brother still live in San Jose. I visited in July and couldn't get over property prices! Too bad....I'd move back in a heart beat if I could afford to. Oh well.

    Thanks a bunch. As soon as I can formulate an intelligent question regarding FX in/outs and inserts, I'll post it.
    Cheeseburgers Rock!

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    Now let me know if I’m way off base here… It’s been a few years…But…

    0 dB is a logarithmical representation of known voltage, or power, across a specific impedance (I’m not exactly sure what that is in the world audio).

    On a VU meter that ranges from 0 to -40, it would be easy to assume that to cut your output in half you would peak your levels at –20. But no; because of the log function of decibels you would set them at –3 to achieve this. In the same manner, if you upgraded your reference amp from 50 watt to 100 watt you wouldn’t double the listening volume, you’d only realize a 3 dB gain. Decibels are generally used to simplify the measurement of power levels. A scale based on the actual voltage would be difficult to understand and would not be as linear as a decibel scale. Many times the term is not used as a finite measurement but as a comparison between to know measurements, like in a dynamic range.

    Jump in any time now…

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    This should scare you -- it's from the faq for the rec.audio.pro newsgroup, located at http://recordist.com/rap-faq/current


    Q3.3 - What is the difference between dBv, dBu, dBV, dBm, dB SPL, and
    plain old dB? Why not just use regular voltage and power
    measurements?
    Our ears respond logarithmically to increases in sound pressure
    level. In order to simplify the calculations of these levels, as
    well as the electrical equivalents of them in audio systems, the
    industry uses a logarithmic system to denote the values.
    Specifically, the decibel is used to denote logarithmic level
    above a given reference. For instance, when measuring sound
    pressure level, the basic reference against which we take
    measurements is the threshold of hearing for the average
    individual, 10^-12 W/m^2. The formula for dB SPL then becomes:
    10 Log X / 10^-12 where X is the intensity in watts per square
    meter
    The first people who were concerned about transmitting audio over
    wires were, of course, the telephone company. Thanks to Ma Bell
    we have a bunch of other decibel measurements. We can use the
    decibel to measure electrical power as well. In this case, the
    formula is referenced to 1 milliwatt in the denominator, and the
    unit is dBm. 1 milliwatt was chosen as the canonical reference
    by Ma Bell. Since P=V^2 / R, we can also express not only power
    gain in dB but also voltage gain. In this case the equation
    changes a bit, since we have the ^2 exponent. When we take the
    logarithm, the exponent comes around into the coefficient, making
    our voltage formula 20 log. In the voltage scenario, the
    reference value becomes 0.775 V (the voltage drop across 600 ohms
    that results in 1 mW of power). The voltage measurement unit is
    dBv.
    The Europeans, not having any need to abide by Ma Bell's choice
    for a canonical value, chose 1V as their reference, and this is
    reflected as dBV instead of dBv. To avoid confusion, the
    Europeans write the American dBv as dBu. Confused yet?



    -- Now that you're confused, go read that Electronic Musician article, I'm sure it's a lot clearer than that.

  9. #9
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    And when measuring radio frequencies (RF), the reference level is 0dBmv (1millivolt at 75 ohms).

  10. #10
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    OPunWide, you're a sick man! Why else would you know that stuff!

    Gidge, as always...you da man with da link!

    MOFO, based on what I've read so far, you're still in the game!

    I've printed out the articles and will stay sober all weekend reading them.
    Thanks guys.

    Gidge, BTW - having this basis to work with (the whole 24/96 sceanrio), that roland studio pak I asked about is a digital weakling compared to the omni studio. Ordered mine yesterday.
    Last edited by getuhgrip; 08-30-2001 at 17:45.
    Cheeseburgers Rock!

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