  Detecting the presence and characteristic scale of a signal is a common
problem in data analysis. We develop a fast statistical test of the null
hypothesis that a Fourier-like power spectrum is consistent with noise. The
null hypothesis is rejected where the local "coefficient of variation"
(CV)---the ratio of the standard deviation to the mean---in a power spectrum
deviates significantly from expectations for pure noise (CV~1.0 for a Chi^2
2-degrees-of-freedom distribution). This technique is of particular utility for
detecting signals in power spectra with frequency-dependent noise backgrounds,
as it is only sensitive to features that are sharp relative to the inspected
frequency bin width. We develop a CV-based algorithm to quickly detect the
presence of solar-like oscillations in photometric power spectra that are
dominated by stellar granulation. This approach circumvents the need for
background fitting to measure the frequency of maximum solar-like oscillation
power, nu_max. In this paper, we derive the basic method and demonstrate its
ability to detect the pulsational power excesses from the well-studied
APOKASC-2 sample of oscillating red giants observed by Kepler. We recover the
cataloged nu_max values with an average precision of 2.7% for 99.4% of the
stars with 4 years of Kepler photometry. Our method produces false positives
for <1% of dwarf stars with nu_max well above the long-cadence Nyquist
frequency. The algorithm also flags spectra that exhibit astrophysically
interesting signals in addition to single, solar-like oscillation power
excesses, which we catalog as part of our characterization of the Kepler light
curves of APOKASC-2 targets.
