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Thread: Measuring random variable wavelength

  1. #1 Measuring random variable wavelength 
    M12
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    Hello everybody,

    I would like to know what methods are there to accurately measure a wavelength created by a random variable, or in other words, a wave which is almost never a perfect sine-wave or similar. I have attached an image illustrating an example, and different points which need to be measured, that can't be dont with a simple "peak-to-peak" or "trough-to-trough" method, because the wave is not perfect.

    How can you measure the wavelength? Are there any mathematical methods that would accurately measure a wavelength?

    http://img97.imageshack.us/img97/683/wave001m.jpg

    Thanks,
    M12.


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  3. #2  
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    Try computing a Fourier series and see which components are dominant.


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  4. #3 Re: Measuring random variable wavelength 
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    Quote Originally Posted by M12
    Hello everybody,

    I would like to know what methods are there to accurately measure a wavelength created by a random variable, or in other words, a wave which is almost never a perfect sine-wave or similar. I have attached an image illustrating an example, and different points which need to be measured, that can't be dont with a simple "peak-to-peak" or "trough-to-trough" method, because the wave is not perfect.

    How can you measure the wavelength? Are there any mathematical methods that would accurately measure a wavelength?

    http://img97.imageshack.us/img97/683/wave001m.jpg

    Thanks,
    M12.
    Your question is meaningless. There is no "wavelength" if you don't have a defined wave.
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  5. #4  
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    Quote Originally Posted by mathman
    Try computing a Fourier series and see which components are dominant.
    This will yield nothing but junk His fundction is not periodic. There is no clear-cut interval over which a periodic version of his function would be naturally modeled. The Fourier series representation is dependent on the interval used to model the function and n fact a Fourier series only applies to a periodic function, i.e. a function defined on a circle. In fact, the Fourier series is nothing more and nothing less than the Fourier transform on the circle group.
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  6. #5 Re: Measuring random variable wavelength 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by M12
    Hello everybody,

    I would like to know what methods are there to accurately measure a wavelength created by a random variable, or in other words, a wave which is almost never a perfect sine-wave or similar. I have attached an image illustrating an example, and different points which need to be measured, that can't be dont with a simple "peak-to-peak" or "trough-to-trough" method, because the wave is not perfect.

    How can you measure the wavelength? Are there any mathematical methods that would accurately measure a wavelength?

    http://img97.imageshack.us/img97/683/wave001m.jpg

    Thanks,
    M12.
    Your question is meaningless. There is no "wavelength" if you don't have a defined wave.
    forgive me but are there not several waves that can be defined in his image, parts of which are denoted by a letter?
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  7. #6 Re: Measuring random variable wavelength 
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    Quote Originally Posted by fatman57
    Quote Originally Posted by DrRocket
    Quote Originally Posted by M12
    Hello everybody,

    I would like to know what methods are there to accurately measure a wavelength created by a random variable, or in other words, a wave which is almost never a perfect sine-wave or similar. I have attached an image illustrating an example, and different points which need to be measured, that can't be dont with a simple "peak-to-peak" or "trough-to-trough" method, because the wave is not perfect.

    How can you measure the wavelength? Are there any mathematical methods that would accurately measure a wavelength?

    http://img97.imageshack.us/img97/683/wave001m.jpg

    Thanks,
    M12.
    Your question is meaningless. There is no "wavelength" if you don't have a defined wave.
    forgive me but are there not several waves that can be defined in his image, parts of which are denoted by a letter?
    No.

    You can doo all sorts of artificial things with an arbitrary function, including various representations in terms of sums of waves. But the definitions and decompositions are subject to various arbitrary assumptions.
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  8. #7  
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    so if you don't mind me asking what is a 'defined' wave?
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  9. #8  
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    Quote Originally Posted by fatman57
    so if you don't mind me asking what is a 'defined' wave?
    It is a wave that has been clearly defined by whoever is talking about it. In this case we don't have one. The terms "wave" and "wavelength" are being bandied about so loosely that it is quite clear that those using the terms in this loose fashion have no idea what they are talking about.

    Without a clear definition, or a situation in which the definitions are well-established by convention, there is little use in trying to have a precise discussion. Lacking a periodic function, or anything that appears to be even a restriction of a known periodic function to some interval, there is no meaning to "wave" or "wavelength".
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  10. #9  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by fatman57
    so if you don't mind me asking what is a 'defined' wave?
    It is a wave that has been clearly defined by whoever is talking about it. In this case we don't have one. The terms "wave" and "wavelength" are being bandied about so loosely that it is quite clear that those using the terms in this loose fashion have no idea what they are talking about.

    Without a clear definition, or a situation in which the definitions are well-established by convention, there is little use in trying to have a precise discussion. Lacking a periodic function, or anything that appears to be even a restriction of a known periodic function to some interval, there is no meaning to "wave" or "wavelength".
    fair enough.

    on another note though I think the OP might be asking how he can first define the wave, maybe an oscilloscope would help but in terms of a mathematical model i think Dr. Rocket might be on the right lines there really...........don't quote me on that though!
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