Isn't noise cumulative? a technical question

Discussion in 'rec.audio.pro' started by Garthrr, Aug 16, 2003.

  1. Garthrr

    Garthrr Guest

    I'd like to try to clarify something for myself and any other dummies like me
    who dont quite get this. I sometime read posts or articles where the writer
    says that the noise figure of a particular peice of gear (for instance, a mic)
    is less than something else (perhaps the noise of the room or another peice of
    gear or whatever).
    Someone might say (and they have) that the noise figure of a particular mic is
    lower than the ambient noise in the room and therefore the mic noise is a
    non-issue. I take this to mean that they are saying that the noise in the room
    sort of swallows up the mic's self noise and nullifies (masks?) it.
    Lets say for example that a mic has 22dBA self noise figure and that the room
    has 40 dBA ambient noise. (excuse me if I am quantifying these figures wrongly)
    I get the impression that the combination of these two noises added together
    would not be 62dBA as would seem logical to me. If the noises did add together
    in that way then I dont believe people would say not to worry about a mic's
    self noise because the room is so much noisier. Instead they would be saying
    that the mic's self noise is just as important in the 40dBA room as it would be
    if the room noise was 20dBA.

    So, I hope I'm getting the context for this question across, even in my clumsy
    way. If I understood enough to ask it right I'd probably know the answer.

    So, does the noise of different links in the chain combine in a linearly
    additive way or is it more complicated than that? For the purpose of this
    question can we set aside the issue of how much noise is actually problematic
    or audible and can we just stick to the theoretical way in which noise combines
    with other noise, all other things being equal?

    Garth~


    "I think the fact that music can come up a wire is a miracle."
    Ed Cherney
  2. Ethan Winer

    Ethan Winer Guest

    Garth,

    > the noise figure of a particular mic is lower than the ambient noise in

    the room and therefore the mic noise is a non-issue ... does the noise of
    different links in the chain combine in a linearly additive way or is it
    more complicated than that? <

    Great question. Noise does add, but when a little noise is added to a lot of
    noise the louder version dominates. Noise from different sources does not
    add the same way as static sound. For example, if you add two sine waves of
    the same level, frequency, and phase, the sum is 6 dB louder than either.
    But adding noise of the same level from two different sources is only 3 dB
    louder. Or thereabouts - I'm not Mr. Math Guy. The reason is because the two
    noise sources are not correlated.

    More relevant to your question is what happens when you add two noise
    sources when one is 10 dB louder than the other, or 20 dB louder, etc.
    Again, I'm not a math guy so I don't have the formula in front of me (though
    it's a very simple formula). But even 10 dB is enough of a difference that
    adding them won't make the result much greater.

    So in your case where the mike's noise is 22 and the room is 40, the sum is
    like 40.1 or something. Certainly not 62! Another factor is the frequency
    distribution. Depending on where you live, room ambient noise is often made
    up of low frequency rumble as well as broadband hiss, unless you have
    forced-air ventilation. Electronic hiss tends to have has more high
    frequency content. So that too affects how the levels combine.

    --Ethan
  3. Arny Krueger

    Arny Krueger Guest

    "Garthrr" <garthrr@aol.com> wrote in message
    news:20030816060742.02537.00000025@mb-m23.aol.com
    > I'd like to try to clarify something for myself and any other dummies
    > like me who dont quite get this. I sometime read posts or articles
    > where the writer says that the noise figure of a particular peice of
    > gear (for instance, a mic) is less than something else (perhaps the
    > noise of the room or another peice of gear or whatever).
    > Someone might say (and they have) that the noise figure of a
    > particular mic is lower than the ambient noise in the room and
    > therefore the mic noise is a non-issue. I take this to mean that they
    > are saying that the noise in the room sort of swallows up the mic's
    > self noise and nullifies (masks?) it. Lets say for example that a
    > mic has 22dBA self noise figure and that the room has 40 dBA ambient
    > noise. (excuse me if I am quantifying these figures wrongly) I get
    > the impression that the combination of these two noises added
    > together would not be 62dBA as would seem logical to me. If the
    > noises did add together in that way then I dont believe people would
    > say not to worry about a mic's self noise because the room is so much
    > noisier. Instead they would be saying that the mic's self noise is
    > just as important in the 40dBA room as it would be if the room noise
    > was 20dBA.


    The correct way to add random uncorrelated noises is to convert the two dB
    values into amplitude, and then take the geometric sum of the two.

    I have a spread sheet that does this.

    In your case the answer is 40.07 dB. IOW the contribution of the 22 dBA mic
    noise is negligible.
  4. Garthrr

    Garthrr Guest

    In article <eh-cnd9anYolj6OiXTWJiw@comcast.com>, "Arny Krueger"
    <arnyk@hotpop.com> writes:

    >n your case the answer is 40.07 dB. IOW the contribution of the 22 dBA mic
    >noise is negligible.


    Thanks Arny, it makes sense now.

    Garth~


    "I think the fact that music can come up a wire is a miracle."
    Ed Cherney
  5. Garthrr

    Garthrr Guest

    In article <BKSdnU0fa6FTm6OiXTWJjg@giganews.com>, "Ethan Winer" <ethan at
    ethanwiner dot com> writes:

    >So in your case where the mike's noise is 22 and the room is 40, the sum is
    >like 40.1 or something. Certainly not 62!


    Yeah I knew it couldnt be, I just couldn't figure out why. That makes sense to
    me now. Sure is great to be able to ask a question like this at 4AM and have an
    answer by 4:30!
    Thanks,
    Garth


    "I think the fact that music can come up a wire is a miracle."
    Ed Cherney
  6. P Stamler

    P Stamler Guest

    A good rule of thumb is that if noise source #2 is about 10 dB less than noise
    source #1 (9.89dB and some change, if you want to be more precise) it will
    raise the combined noise by 1dB, all other factors being equal. Since that's
    considered the "just noticeable difference" in this context, in practice any
    time the second noise source is more than 10dB down from the first, as a rule
    of thumb you don't have to worry about it.

    Peace,
    Paul
  7. On Sat, 16 Aug 2003 15:25:05 GMT, walkinay@thegrid.net (LeBaron &
    Alrich) wrote:

    > Beautifully asked question.


    Hear, hear. I especially liked the part:
    " If I understood enough to ask it right I'd probably know the
    answer."
    Real wisdom there.



    Chris Hornbeck
    http://www.votetoimpeach.org/
  8. Actually, 1dB is a 26% increase in power. So (assuming noise powers add
    linearly), source #2 would actually have to be only 6dB down for a 1dB increase
    in noise level.


    > A good rule of thumb is that if noise source #2 is about 10 dB less than noise
    > source #1 (9.89dB and some change, if you want to be more precise) it will
    > raise the combined noise by 1dB, all other factors being equal. Since that's
    > considered the "just noticeable difference" in this context, in practice any
    > time the second noise source is more than 10dB down from the first, as a
    > rule of thumb you don't have to worry about it.
  9. Arny Krueger

    Arny Krueger Guest

    "P Stamler" <pstamler@aol.com> wrote in message
    news:20030816110200.28604.00000130@mb-m18.aol.com

    > A good rule of thumb is that if noise source #2 is about 10 dB less
    > than noise source #1 (9.89dB and some change, if you want to be more
    > precise) it will raise the combined noise by 1dB, all other factors
    > being equal.


    My handy-dandy spread sheet says that the contribution from a source 10 dB
    smaller than the larger source is about 0.5 dB - actually more like 0.4 dB.

    To be precise, if you mix a noise signal at -20 dB with a noise source
    at -30 dB, the sum is -19.5861 dB.

    This result is consistent at other levels, for example if you mix a noise
    signal at -80 dB with a noise source at -90 dB, the sum is -79.5861 dB.

    My estimate of a 0.5 dB increase is based on the fact that uncorrelated
    noise is properly added geometrically, which involves taking the square root
    of the sum of the squares.

    To get a 1 dB increase you have to mix noises that are about 6 dB apart.
  10. P Stamler

    P Stamler Guest

    Right you are, Bill and Arny. Sorry -- forgot to take a square root while I was
    calculating. In reality, if signal #2 is 5.868dB or so below signal #1, it will
    add 1dB to the cumulative noise. So anything less than that, all things being
    equal, is not worth bothering with or worrying about.

    Peace,
    Paul
  11. Mike Rivers

    Mike Rivers Guest

    In article <uPKdnUbpnZoQb6OiXTWJhw@comcast.com> arnyk@hotpop.com writes:

    > My handy-dandy spread sheet says that the contribution from a source 10 dB
    > smaller than the larger source is about 0.5 dB - actually more like 0.4 dB.


    How about if you mix noise with music? Does it depend on how much the
    music sounds like noise? <g>



    --
    I'm really Mike Rivers - (mrivers@d-and-d.com)
  12. Arny Krueger

    Arny Krueger Guest

    "P Stamler" <pstamler@aol.com> wrote in message
    news:20030817120002.07650.00000065@mb-m25.aol.com

    > Right you are, Bill and Arny. Sorry -- forgot to take a square root
    > while I was calculating. In reality, if signal #2 is 5.868dB or so
    > below signal #1, it will add 1dB to the cumulative noise. So anything
    > less than that, all things being equal, is not worth bothering with
    > or worrying about.


    I agree that this is a good rule of thumb. Somehow I hadn't thought of the
    problem exactly that way.

    Of course one has to remember the underlying presumptions, one of which is
    that both noises have the same spectral balance. In real life this is not
    the case much of the time. If you mix two noises with significantly
    different spectral balance (i.e., pink and white) the contribution of the
    source with lower amplitude may be more or less audible.

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