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Dumb question about white noise

  1. Jan 1, 2007 #1

    Math Is Hard

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  2. jcsd
  3. Jan 1, 2007 #2

    DaveC426913

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    The amplitude of the signal ranges from -1 to+1. The range is completely relative, thus there are no units. If you produced a graph that went from -.5 to +.5, your white noise would simply be quieter.

    What is important about white noise is not the amplitude, but the frequencies.
     
    Last edited: Jan 1, 2007
  4. Jan 1, 2007 #3
    Actually in communication engineering, what is most important is the power of the noise, mainly to calculate the signal-to-noise ratio of the system.

    btw why is the frequency important, isn't nearly constant for all frequencies?
     
  5. Jan 1, 2007 #4

    Hurkyl

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    DaveC was talking about the definition -- amplitude is irrelevant and frequency spectrum is everything, if the question is "is this white noise?"
     
  6. Jan 1, 2007 #5

    Gokul43201

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    You might want to start with first understanding what measurement noise is.

    Let's say I'm trying to measure the average volume (power) of sound produced inside a room inhabited by some specified number of teenaged girls on cellphones. I've got a mic located at some point in the room that recording the complex jumble of "how cute"s and "and she's like"s. Now, the mic (and associated instrumentation) converts the audio input into an electric signal, which ultimately can be stored as an array of numbers.

    Now the circuit that converts the audio signal to a voltage is not ideal. The resistors in the circuit, for instance, do not maintain a perfectly constant resistance. Their resistance fluctuates ever so slightly, due to thermal effects. This introduces "noise" into the voltage signal. This noise turns out to be white, as it has no specific frequency dependence (this may become more clear after the next bit).

    In addition to the noise from the circuitry, another source of noise may be, say noise from a nearby construction site, with a jackhammer going off at 100Hz. This type of noise is not considered white, because it happens more at certain frequencies (in this case, around 100Hz) than others, and so, can be identified and eliminated mathematically.

    So, if you looked at your data as total sound power vs time, you'll see that it has fluctuations about some average value. These fluctuations will include among other things, the 100Hz input from the jackhammer. If this (jackhammer) signal is small compared to the total size of the voise, you won't easily notice it, just by looking at signal vs time. However, if you decompose your noise into "bins" of different frequencies, you'll notice that while much of it has no prefered frequency (and is hence called white), there's a clear peak at around 100Hz that tells you about the jackhammer.
     
    Last edited: Jan 1, 2007
  7. Jan 1, 2007 #6

    Math Is Hard

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    Thanks all. I think where I am getting tangled up is that I am looking at the amplitude of the wave form and trying to relate it to decibels, which is clearly not the way I should be thinking about it.
     
  8. Jan 2, 2007 #7

    DaveC426913

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    Man, you guys like to confuse things...
    I'm all for opportunities for further education but shouldn't we be sure the OP gets his confusion cleared up first?:rolleyes:
     
  9. Jan 2, 2007 #8

    Math Is Hard

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    ahem.. her confusion. :wink:
     
  10. Jan 3, 2007 #9

    DaveC426913

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    Her confusion. :blushing:
     
  11. Jan 3, 2007 #10

    Math Is Hard

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    I hope you folks don't mind, but I want to ask some little peripherially related questions as I work through this. The first one:
    When a singer sings a high C note (one octave above middle C) , and a flute player plays this same note, what property makes the difference in how I can tell the two apart?
     
  12. Jan 3, 2007 #11

    DaveC426913

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    A pile of things.

    One is harmonics, the property of instruments whereby higher multiples of the same frequency are produced (I think only electronics can produce a pure tone with no harmonics).

    Another is the tone, which is in large part determined by the shape of the wave. There are square waves, sinusoidal waves triangle waves, etc.

    Some examples:
    http://whorld.org/Help/images/Waveforms.gif

    The sinusoidal wave will produce a very pure, round yet lifeless tone. The square will produce a harder, but still full tone. The pulse is the same as a square, but will produce a thinner, reedier tone.
     
    Last edited: Jan 3, 2007
  13. Jan 3, 2007 #12

    Gokul43201

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  14. Jan 3, 2007 #13

    Math Is Hard

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    Thank you. This is really, really, really helpful. Another question: Say, I took a digital recording sample of a flute player playing a single note, and then made a copy of it. if I played the two sound files back simultaneously (perfectly synchronized), would I be able to distinguish if there are two notes playing rather than one?
     
    Last edited: Jan 3, 2007
  15. Jan 3, 2007 #14

    DaveC426913

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    You can try this easily enough. Put on a set of headphones and listen to some music. In stereo, you should be able to hear two sides, L and R. Switch it to mono and you will no longer be able to hear two sides; it will sounds as if there is one source of sound, dead centre.

    Or are you thinking about the diff between the original and the digital? Well, I guess that depends on the sampling rate (and thus fidelity) of the digital recording. high enough, and you won't know the diff. The lower you go, the more likely you'll hear a slight diff.
     
  16. Jan 3, 2007 #15

    Hurkyl

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    Hrm. Isn't the shape of the wave completely determined by its harmonic content?
     
  17. Jan 3, 2007 #16

    berkeman

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    Sort of. There is also the time-relationship of the harmonics. I did some work a while back synthesizing musical tones, and the time (phase) relationship of the harmonics makes a difference in how the tone sounds. Like, with the 1/x odd harmonics you can make a square wave with the correct phase relationships, right? But if you slide the phases of the harmonics, you no longer get a square wave, and its tone is different. Weird when you think about it....
     
  18. Jan 4, 2007 #17

    berkeman

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    Oh, and there are the attack, decay and vibrato elements to the "sounds". Those make very big differences in being able to identify instruments and sounds, and contribute hugely to "nice sounding" tones and notes that you synthesize.
     
  19. Jan 4, 2007 #18

    Hurkyl

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    Hrm, good point. Are the harmonics of an actual instrument out of phase with the fundamental like that?
     
  20. Jan 4, 2007 #19

    berkeman

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    What I saw in my experiments and synth work was that the harmonics move through in phase. The waveforms are not stable in a shape sense. I think it's because the attenuation of a stroked string note, for example, is dependent a bit on the harmonic frequency. So when you pluck a guitar string, you get an initial waveform, but that changes over time as the different harmonics attenuate at different rates, and the waveform shape of the actual sound note changes a lot throughout the duration of the note.

    As a related aside -- the frustrating thing is to try to reproduce the sounds of musical instruments with synthesized sounds. Even if you record part of a note from an instrument, trying to get the attack and decay part of a transitory note right is really a challenge. Fun stuff, but very challenging. (I never got real good at it, BTW, but definitely developed an appreciation for how much stuff is involved.)
     
  21. Jan 7, 2007 #20

    Math Is Hard

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    Thanks for the responses. I haven't forgotten about you guys - I just want to read some more and then I'll be back with more questions.
    This summer we read a little bit about information theory and signal detection in a class I took, and I got interested in learning more about it. I'm reading a book right now called Noise by Bart Kosko. It's a fun pop-sci read, but he tends to vacillate between too much detail and not enough (for a layperson, anyway) so I find myself getting lost.
     
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