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\section{Introduction}  Turbulence in the interstellar medium is ubiquitous and self-similar across many orders of magnitude \citep[]{brandenberg13}. Within molecular clouds, turbulence appears to play an essential role in the star formation process, regulating the efficiency at which stars form, seeding filaments and over-densities, and even potentially setting the stellar initial mass function \citep{padoan13,Offner14}. \citep{padoan13,Offner14ppvi}.  While the presence of supersonic motions is readily verified and has been studied using molecular spectral lines for several decades \citep{larson81}, the origin, energy injection scale, means of sustenance, and rate of dissipation remain debated. Moreover, molecular clouds display significant variation in bulk properties, ongoing star formation, and morphology. Consequently, it seems highly likely that these differences impact the turbulent properties of the gas and leave signatures — but if so they are difficult to identify observationally. Detailed study of the turbulence within molecular clouds is confounded by a variety of factors including observational resolution, projection effects, complex gas chemistry, and variable local conditions \citep[e.g.,][and references therein]{beaumont13}. Any one molecular tracer only samples a limited set of gas densities and scales, so that reconstructing cloud kinematics reliably involves assembling a variety of tracers across different densities and scales \citep[e.g.]{gaches15}.  %The gas also changes phase when it is dissociated or ionized,  Many studies of cloud structure instead rely on a single gas tracer like CO, which is bright and exhibits widespread emission that reflects the underlying H$_2$ distribution \citep{bolatto13,heyer15}. Connecting such emission data to underlying turbulence and bulk cloud properties, however, is non-trivial. A variety of statistics have been proposed throughout the literature to characterize spectral data cubes and distill the complex emission information into more manageable 1D or 2D forms \citep[e.g.,]{heyer97,rosolowsky99,rosolowsky08,burkurt09}. However, in most cases, the utility of the statistic and its interpretation is not well constrained.  Numerical simulations, which supply full 6-D information $(x,y,z, v_x, v_y, v_z)$, provide a means to study turbulence and constrain cloud properties. Prior studies have investigated how the turbulent power spectrum, inertial driving range, and fraction of compressive motions have influenced star formation \citep{klessen01,bate09b,federrath08}. Other studies have connected simulated turbulent properties to observables such as CO emission by performing radiative post-processing \citep[e.g.,]{padoan01,bertram14}. In some cases, this procedure is able to identify theoretical models that have good agreement with a given observation. Consequently, the most effective way to study turbulence in molecular clouds is by comparing observations with ``synthetic observations", in which the emission from the simulated gas is calculated via radiative transfer post-processing \citep{Offner2008b,Offner12}. Recently, \citep{yeremi14} and \citp{koch15} Koch et al. 2015  performed parameter studies of magnetohydrodynamic simulations in order to assess the sensitivity of common astrostatistics to changes in cloud velocity dispersion, virial parameter, driving scale, and magnetic field strength. They found that some statistics were responsive to changes in the temperature, virial parameter, mach Mach  number and inertial driving range. These results suggest that certain statistics may also be sensitive to energy input and environmental variation due to ongoing star formation. One fundamental puzzle in star formation is why the efficiency at which dense gas forms stars is only a few percent per free fall time \citep[][and references therein]{krumholz14}. Early three-dimensional hydrodynamic simulations discovered that supersonic turbulence decays rapidly and predicted that without additional energy input turbulence should decay significantly within a dynamical time \citep{ostriker98,maclow99}. This implies that gravity should be able to efficiently form stars after a dynamical time. However, turbulence observed within molecular clouds does not appear to weaken and star formation efficiencies are small after several dynamical times \citep{tmk07}. \citep{KandT07}  One explanation for the longevity of observed turbulence is that motions are driven internally via feedback from forming or evolved stars \citep[][and references therein]{krumholz14ppvi}. In principle this should introduce a characteristic energy input scale \citep{frank10,hansen12,Offner15}, \citep{carroll09,hansen12,Offner15},  which should impact turbulent statistics. However, from an observational prospective, stellar feedback is {\it messy} and identifying clear feedback signatures is complex for the reasons mentioned above. %Analysis is typically restricted by the assumption that the velocities and extent along perpendicular directions are s Disentangling feedback signatures from the turbulent background and assessing their role is challenging since any low-velocity motions excited by feedback are lost in the general cloud turbulence \citep{swift08,arce10,arce11}.   In this paper, we aim to extend the study by \citep{koch15} by applying a suite of turbulent statistics to simulations with feedback from stellar winds. The simulated stellar winds produce parsec scale features and excite motions of several $\kms$ as a result of their expansion \citep{Offner15}. While protostellar outflows may also leave imprints in the turbulent distribution, winds appear to inject more energy on larger scales which leaves a more distinct imprint on the gas velocity distribution \citep{arce11}. By performing synthetic observations, we aim to identify discriminating statistical diagnostics to apply to observed clouds that can identify and constrain feedback: the ``smoking gun".