Parametric analysis of frequency domain reflectometry measurements

In the frequency domain reflectometry (FDR) method of remotely measuring discontinuities in telephone lines, the reflected amplitude versus frequency trace resulting from a single fault has a sinusoidal form that decays with increasing frequency. Each additional fault adds a decaying sinusoidal component with frequency and decay rate in proportion to the fault distance. The objective is to be able to resolve closely spaced faults that are located far from the measuring instrument. Our conventional approach has been to use Fourier analysis, however, we are forced to discount highly accurate low frequency information because a Blackman window is needed to minimize spectral leakage. As an alternative, we assumed an autoregressive (AR) model with a complex pole pair associated with each decaying sinusoidal component and then calculated model parameters using the Burg method [3]. As the model order was increased the Burg method yielded better resolution than the Fourier transform but it suffered from spurious peaks and spectral line splitting when the model order was too high. With an unknown number of line faults, there was no clear way to pre-select the order of the model. We also tried analysis by successive decomposition of the trace assuming decaying sinusoids and using a least squares metric. At the end, we reverted to the Fourier transform and used a mirrored extension of the trace data set. We also used a variety of mirror points at the low frequency end of the trace. Although not fully satisfactory, this has given the best results to date.