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Best way to measure precise harmonics?

Discussion in 'Electronic Design' started by eromlignod, Oct 18, 2007.

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  1. eromlignod

    eromlignod Guest

    Hi guys:

    I need to find the component harmonic frequencies of an AF wave and I
    need for it to be pretty precise (+/- .001 Hz or so). I have access
    to a spectrum analyzer, but it just doesn't seem to be precise enough
    (or I'm using it wrong). It gives me peaks in a frequency domain, but
    they are not pinpoint lines, ostensibly due to a limited-sample FFT.

    Are there any other devices or methods to obtain accurate frequencies
    of each harmonic to three decimal places? Thanks for any suggestions
    you might have.

    Don
     
  2. Tunabe filer - amplifier - frequency counter.
    Something is strange in your setup, for sure
    if the fundamental frequnecy is known, then the harmonics WILL be an exact
    multiple of that.
    If the fundamental frequency changes (is FM modulated), then you have a problem.
    The question then comes up: What are you measuring, and why the accuracy?
     
  3. Phil Allison

    Phil Allison Guest

    ** Google Groper Alert !!!!!!


    ** That is DAMN precise !!!

    You need to justify that or be considered a NUT case.


    ** Meaningless, to just drop that title with no explanation.


    ** Poor diddums.............


    ** Hang on, YOU just asked for 6 or 7 decimal places of accuracy.

    Got a clue what the term means ????



    ** Don't tempt me.



    ........ Phil
     
  4. John Larkin

    John Larkin Guest

    Measure the fundamental frequency with a counter. The harmonic
    frequencies are precise integer multiples of that.

    John
     
  5. eromlignod

    eromlignod Guest


    Yeah, yeah...go **** yourself, asshole.

    I'm dealing with the vibration of piano strings which go as low as
    27.5 Hz. Pianos are routinely tuned to less than one "cent" of
    deviation, which, at 27.5 Hz, amounts to about .016 Hz. That's just
    to get it in tune for music. I need to be a little finer than that.

    Currently I can measure the fundamental of the low note theoretically
    to about 1/1000th of a cent. Actually I measure the period of the
    wave by counting the vibrations of a 50 MHz oscillator compared to the
    vibration of the string. But I have found that natural fluctuations
    in the pitch of the string as it vibrates don't really allow you to
    measure much better than a tenth of a cent or so.

    I'm developing a method of string manufacture to control individual
    harmonics relative to each other, so I need to be able to accurately
    see their relative frequencies (or periods).

    I was hoping there might be a common device or method for this.
    Otherwise I'll just have to filter and use my present device.

    Don
     
  6. Well you could generate a near sine wave oscillator,
    with adjustable frequency, I'd use a computer to
    generate that, then mix that with your output.
    Filter out everything except +/- 1 hz, and measure
    that amplitude relative to inputs.
    I'm suggesting a very high Q notch filter, that uses
    hetrodyning.
    Sounds like fun.
    Ken
     
  7. John Larkin

    John Larkin Guest

    As you say, the frequency of a vibrating string varies with time, so
    the exact frequency isn't a single value, and will also vary as a
    function of initial amplitude.

    I know a guy who makes handbell sets. He uses an n/c lathe, a striking
    hammer, a microphone, and a computer that does fft's and things and
    closes the machining loop to tune all the not-quite-integral harmonics
    for best sound. He's learned a lot about this sort of thing. If you're
    interested, I could put you into contact with him.

    John
     
  8. colin

    colin Guest


    to get 0.001 hz resolution you need to sample it for something like 1000
    seconds.

    you can then do an an FFT, maybe with a soundcard or dsp micro etc.
    or you can mix it with a known frequency and detect the beat,
    but the beat frequency will be as low as 0.001 hz.

    alternativly you can measure the period instead,
    this would involve filtering out the frequency you want,
    making it digital and feeding it into a period averaging meter
    eg hp-5328b universal frequency counter.

    this will give you 0.00001 % resolution or better averaged over 1
    second but the acuracy will probably depend entirly upon how well you filter
    the signal and the resultant snr.

    Colin =^.^=
     
  9. eromlignod

    eromlignod Guest

    Don

    Thanks, John. Yeah, you might want to send me his info. Sounds like
    he's doing something very similar.

    I guess I should have posted a desired accuracy of "1/10 cent", which
    is a logarithmic term that is relative to the frequency in question.
    But I wasn't sure if everyone would be familiar with that
    nomenclature, since it's primarily a musical term. Actually, 0.001 Hz
    would be an absolute worst case for the lowest fundamental. Cents get
    exponentially larger (in terms of Hz) as you go up in pitch.

    Incidentally, I sustain the note with an "Ebow"-like magnetic
    sustainer, so decay is not a factor, since the note vibrates
    continuously at a steady amplitude. I still get variations of 1/10th
    cent or more, though some of that might be the oscillator crystal.

    Don
     
  10. That kind of accuracy requires very high quality
    components. For example a 100 ohm resistor
    with vary slightly with current, likewise a 100 uF
    cap will vary depending on the stored voltage.
    There are ways to compensate for that, but they
    take time.
    Better keep an eye on that bottom line, cost-
    benefit ratio.
    What's the application?
    Ken
     
  11. Bad news. Piano harmonics are not exact integer multiples. See:
    <http://en.wikipedia.org/wiki/Harmonic_series_(music)>
    especially the section on "harmonics and tuning". If it were exact
    integers, it would be easy.
    <http://en.wikipedia.org/wiki/Piano_tuning>

    In college, I attempted to tune an upright piano using an ancient HP
    nixie tube counter to its limits of accuracy using exact harmonic
    overtone series frequencies. It sounded "dead" and generally lousy. I
    was later rescued by a professional piano tuner who explained how it
    works. I've tuned 4 pianos since then, with varying degrees of effort
    and success.

    What he's apparently (not sure) trying to do is mimick the art of the
    piano or string instrument tuner. That's going to be rough because
    the very best piano tuners adjust their tuning for the type of music
    to be played, the acoustics of the concert hall, and the expected
    length of time between tuning and the actual concert. Basic guides,
    such as:
    <http://piano.detwiler.us/index.html>
    are a great start. However, using a modified guitar tuner directly is
    not going to result in the correct harmonic partials. Note the above
    instructions say to ignore the piano tuner and rely on the beat notes.

    My best guess(tm) is that it's going to take filters (to remove the
    fundamental) and a period counter to do this.
     
  12. The FFT sample length just determines the bin width of the FFT output
    array. There are more fundamental problems with your idea (one aspect
    of it addressed by Colin): any disturbance will broaden the _ACTUAL_
    signal width to beyond most common FFT bin widths. Acoustic noise,
    atmospheric pressure variations, electric interference, all contribute
    to this signal broadening. As do ambient temperature and other things I
    can't think of at the moment...

    You're asking to do something that can't be done.

    Now, this is more nearly feasible, and was addressed by Colin...
    Actually, I think the figure is more like 4000 seconds...

    And here is the only possibility of doing what you want; get the broad
    signal peaks using a high-resolution spectrum analyzer, and find the
    peak bin of each harmonic within its (probably many bin-width) hump. If
    you're lucky, and in a very quiet acoustical environment, and there's
    very little electrical noise, and the moon is in exactly the right
    place, and you've sacrificed the right set of chickens, you may be able
    to see a single bin that's a tiny bit higher than the others.

    As to whether this will really mean anything, I couldn't say. I really
    doubt it.
    Personally, I doubt that this will give anything useful, even if you can
    overcome the instrumentation setup issues.

    John Perry
     
  13. Measure the fundamental. And good luck with that. With piano (or other
    stringed instrument) the decay of the harmonics and possibly some phase
    shifts over time will introduce errors at the .001 Hz level.
     
  14. Not even wrong.

    Piano string overtones are NOT exact multiples of the fundamental, due
    to the lateral stiffness of strings.

    An "exactly tuned" piano will thus sound awful.

    Instead, the piano keyboard is "stretched", going something like 38
    cents or so low on the low end and 12 cents or so high on the high end.

    Since the enharmonic overtone relation of a string is well known, the
    overtone frequencies are strictly locked to the fundamental. And thus
    precisely defined.

    Constult any standard piano tuning book for details.

    --
    Many thanks,

    Don Lancaster voice phone: (928)428-4073
    Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
    rss: http://www.tinaja.com/whtnu.xml email:

    Please visit my GURU's LAIR web site at http://www.tinaja.com
     
  15. Tom Bruhns

    Tom Bruhns Guest

    One of the problems you'll have is the length of time over which you
    can make your measurement. To nail a frequency as accurately as you
    want, if you don't know something a priori about it, you need to
    observe it for a long time. Will the strings vibrate for 1000
    seconds? If not, then realize that you are not dealing with a single
    frequency but a spectral density. The attack and decay envelopes
    modulate the string's natural frequency.

    I can pretty easily measure frequencies in the audio range to 0.001Hz
    resolution, IF they stick around long enough. FFT-based spectrum
    analyzers worth having should have "zoom" capability, allowing you to
    set essentially any center frequency you want and then set the span
    very low. _IF_ you have a priori knowledge that the signal you are
    looking at is a pure sinewave (that is, will maintain the same
    amplitude for a long time and is not polluted by other signals at
    other frequencies), you can very accurately determine its frequency in
    a much shorter time. That's because you can measure the period of a
    relatively small number of cycles. But any other signals, especially
    ones not harmonically related to the tone you're looking at, will mess
    up the waveform so that the period from zero crossing to zero crossing
    is not constant from one cycle to the next. Ultimately, you'll be
    limited by inevitable noise that will cause the same problem.

    I have a frequency counter that finds low frequencies by the method of
    inverting the waveform's period (or the period of multiple cycles),
    but I can still get better accuracy in a given time using an FFT-based
    spectrum analyzer, and have the added benefit of being able to observe
    the shape of the FFT'd input spectrum, which gives confidence that the
    signal is (or isn't) clean enough to use for accurate frequency
    measurement. With an Agilent 89410 analyzer, I can get a 3200 point
    FFT with 1Hz span centered down to 1 millihertz resolution, but at
    that span and than number of points, it takes llllooooong time to
    make a measurement. On the other hand, with that a priori knowledge
    about the signal, I can resolve easily a tenth of the spacing between
    FFT points, knowing the details of the windowing function (which
    determines the filter shape that each FFT point represents).

    Cheers,
    Tom
     
  16. Tom Bruhns

    Tom Bruhns Guest

    One of the problems you'll have is the length of time over which you
    can make your measurement. To nail a frequency as accurately as you
    want, if you don't know something a priori about it, you need to
    observe it for a long time. Will the strings vibrate for 1000
    seconds? If not, then realize that you are not dealing with a single
    frequency but a spectral density. The attack and decay envelopes
    modulate the string's natural frequency.

    I can pretty easily measure frequencies in the audio range to 0.001Hz
    resolution, IF they stick around long enough. FFT-based spectrum
    analyzers worth having should have "zoom" capability, allowing you to
    set essentially any center frequency you want and then set the span
    very low. _IF_ you have a priori knowledge that the signal you are
    looking at is a pure sinewave (that is, will maintain the same
    amplitude for a long time and is not polluted by other signals at
    other frequencies), you can very accurately determine its frequency in
    a much shorter time. That's because you can measure the period of a
    relatively small number of cycles. But any other signals, especially
    ones not harmonically related to the tone you're looking at, will mess
    up the waveform so that the period from zero crossing to zero crossing
    is not constant from one cycle to the next. Ultimately, you'll be
    limited by inevitable noise that will cause the same problem.

    I have a frequency counter that finds low frequencies by the method of
    inverting the waveform's period (or the period of multiple cycles),
    but I can still get better accuracy in a given time using an FFT-based
    spectrum analyzer, and have the added benefit of being able to observe
    the shape of the FFT'd input spectrum, which gives confidence that the
    signal is (or isn't) clean enough to use for accurate frequency
    measurement. With an Agilent 89410 analyzer, I can get a 3200 point
    FFT with 1Hz span centered down to 1 millihertz resolution, but at
    that span and than number of points, it takes llllooooong time to
    make a measurement. On the other hand, with that a priori knowledge
    about the signal, I can resolve easily a tenth of the spacing between
    FFT points, knowing the details of the windowing function (which
    determines the filter shape that each FFT point represents).

    Cheers,
    Tom
     
  17. Jim Thompson

    Jim Thompson Guest

    If these are wire strings, might one simply excite them with a small
    signal... say an AGC'd oscillator loop, then measure the frequency
    with a counter?

    ...Jim Thompson
     
  18. John Larkin

    John Larkin Guest

    If you've got a steady-state oscillation, a simple frequency counter
    should do just fine. Even a cheap crystal timebase will be stable to a
    ppm per month, often a ppm per year.

    I wonder what the tempco of a steel string will be. That's probably
    the dominant thing that walks the frequency around. 10, 20 PPM/K?

    Say, how does the sound of a piano change with temperature? All that
    wood and steel must move around a lot.

    Email me for the contact. jjlarkin atsign highlandtechnology dthing
    cthing.


    John
     
  19. eromlignod

    eromlignod Guest


    Please read all of my posts in this thread. I have infinite sustain
    time and I don't need to use a frequency counter to determine
    frequency. The frequencies are much too low for that. I can measure
    the period in the time of one vibration of the string (<40ms) and it
    is much more accurate.

    Don
     
  20. eromlignod

    eromlignod Guest


    I already know all of this. I'm not tuning a piano, I'm analyzing the
    individual harmonics of a string.

    Don
     
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