  Spin-bath noise characterization, which is typically performed by multi-pulse
control sequences, is essential for understanding most spin dynamics in the
solid-state. Here, we theoretically propose a method for extracting the
characteristic parameters of a noise source with a known spectrum, using a
single modified Hahn-echo sequence. By varying the application time of the
pulse, measuring the coherence curves of an addressable spin, and fitting the
decay coefficients to a theoretical function derived by us, we extract
parameters characterizing the physical nature of the noise. Assuming a
Lorentzian noise spectrum, we illustrate this method for extracting the
correlation time of a bath of nitrogen paramagnetic impurities in diamond, and
its coupling strength to the addressable spin of a nitrogen-vacancy center.
Considering a realistic experimental scenario with $5\%$ measurement error, the
parameters can be extracted with an accuracy of $\sim 10 \%$. The scheme is
effective for samples having a natural homogeneous coherence time ($T_2$) up to
two orders of magnitude greater than the inhomogeneous coherence time
($T_2^*$), and mitigates technical noise when further averaging is irrelevant.
Beyond its potential for reducing experiment times by an order-of-magnitude,
such single-pulse noise characterization could minimize the effects of long
time-scale drifts and accumulating pulse imperfections and numerical errors.
