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?