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Thread: Weighted Harmonic Mean with Zero Value

  1. #1
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    Weighted Harmonic Mean with Zero Value

    I have an output from a noisy signal, saved as a set of cosines.
    I have a set of frequencies from 0to x Hz (x is a large number), and a set, of the same size, of amplitudes.
    I want to work out the weighted harmonic mean of the frequencies present, when the weighting of the frequency is the magnitude of the corresponding amplitude.
    For example: If I have a set of frequencies [ 1 , 2 , 3] and amplitudes [ 10, 100, 1000 ](such that the cosine with frequency 1 hasamplitude 10, etc.). Then, the harmonic mean of the frequencies is 2.8647.
    However, I run into problems when I have a zero frequency (a "DC" component) - the weighted harmonic mean is just zero due to a single infinite value in the denominator!
    The real life problem is a very big set of cosines, starting with a zero frequency, going up to several GHz. Much of the signal is weighted in a portion of the spectrum and I want to compare a simple weighted mean of the spectrum with a harmonic mean.
    The way around this (it seems a cheap way) is to ignore the zero frequency - it is only one frequency out of tens of thousands. But is there a correct way to do this?


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  2. #2
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    Re: Weighted Harmonic Mean with Zero Value

    just a thought - is the following a suitable "botch"?

    If I add a set value (say 1) to every frequency in the set, so there is no zero value, THEN find the weighted average, THEN subtract 1 from the answer

    would this give a valid result (a quick back of the envelope calc yields different results for different additions yeilds different results, so maybe not !)
    Last edited by weesam; Dec 29th 2016 at 04:16 AM.
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  3. #3
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    Re: Weighted Harmonic Mean with Zero Value

    the frequency of 0 Hz is just the DC component of the signal.

    It generally doesn't carry any information and input signals are regularly DC shifted and scaled to account for the input and output ranges of various components.

    So in short, unless you have good reason not to, ignore the 0Hz component.
    Thanks from weesam
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