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Here we test the Stochastic Dynamic Operator (SDO) as a new framework for describing physiological signal dynamics relative to spiking or stimulus events. The SDO is a natural extension of existing spike-triggered average (STA) or stimulus-triggered average techniques currently used in neural analysis. It extends the classic STA to cover state-dependent and probabilistic responses where STA may fail. In simulated data, SDO methods were more sensitive and specific than the STA for identifying state-dependent relationships. We have tested SDO analysis for interactions between electrophysiological recordings of spinal interneurons, single motor units, and aggregate muscle electromyograms (EMG) of major muscles in the spinal frog hindlimb. When predicting target signal behavior relative to spiking events, the SDO framework outperformed or matched classical spike-triggered averaging methods. SDO analysis permits more complicated spike-signal relationships to be captured, analyzed, and interpreted visually and intuitively. SDO methods can be applied at different scales of interest where spike-triggered averaging methods are currently employed, and beyond, from single neurons to gross motor behaviors. SDOs may be readily generated and analyzed using the provided SDO Analysis Toolkit We anticipate this method will be broadly useful for describing dynamical signal behavior and uncovering state-dependent relationships of stochastic signals relative to discrete event times. Significance Statement Here the authors introduce new tools and demonstrate data analysis using a new probabilistic and state-dependent technique, which is an expansion and extension of the classical spike-triggered average, the Stochastic Dynamic Operator. Stochastic Dynamic Operator methods extend application into domains where classical spike-triggered averages fail, capture more information on spike correlations, and match or outperform the spike-triggered average when generating predictions of signal amplitude based on spiking events. A data and code package toolkit for utilizing and interpreting Stochastic Dynamic Operator methods is provided together with example simulated and physiological data analyses. Both the method and the associated toolkit are expected to be broadly useful in research domains where the spike triggered average is currently used for analysis, and beyond., (Copyright © 2024 Smith et al.)