  Researchers have observed that the frequencies of leading digits in many
man-made and naturally occurring datasets follow a logarithmic curve, with
digits that start with the number 1 accounting for $\sim 30\%$ of all numbers
in the dataset and digits that start with the number 9 accounting for $\sim
5\%$ of all numbers in the dataset. This phenomenon, known as Benford's Law, is
highly repeatable and appears in lists of numbers from electricity bills, stock
prices, tax returns, house prices, death rates, lengths of rivers, and
naturally occurring images. In this paper we demonstrate that human speech
spectra also follow Benford's Law on average. That is, when averaged over many
speakers, the frequencies of leading digits in speech magnitude spectra follow
this distribution, although with some variability at the individual sample
level. We use this observation to motivate a new set of features that can be
efficiently extracted from speech and demonstrate that these features can be
used to classify between human speech and synthetic speech.
