The Coherent Structure Detector, developed by the authors in several recent papers, provides a rigorous statistical technique for detecting coherent structures in signals, especially in the atmospheric boundary layer, such as eddies, gust, and so on. Unfortunately, this approach uses continuous-time wavelets and describes the time series in a frame instead of a basis. This complicates the time-scale filtering needed to characterize the shape of the detected coherent structures. To allow time-scale filtering, in this paper we apply the discrete wavelet transform and represent the time series in a basis. Wavelet shrinkage, with thresholds based on the Coherent Structure Detector, is then applied to time-scale filter out the incoherent signal components. Conditional sampling techniques then estimate the shape of coherent structures by designing an optimal matched filter, which has a direct interpretation and implementation in the discrete wavelet basis. The technique is demonstrated with measurements from thunderstorm outflows.