Improved spectrum estimation from digitized time series on a logarithmic frequency axis

We present a practical technique for spectrum and spectral density estimation from long time series by Fourier transforms. We apply Welch’s popular technique of “averaging over modified periodograms” which uses Fourier transforms of fixed length with time-domain windows and overlap. Our technique retains the basic properties of this method, but computes the optimal frequency resolution individually for each Fourier frequency on a logarithmic frequency axis, thus yielding results that are more useful than those of the standard techniques.