Event-Related Warping: A Toolbox for Temporal Alignment and Jitter Correction in Sequential Experimental Paradigms

Sequential experimental paradigms are fundamental to cognitive neuroscience, yet standard event-related response analysis struggles with the temporal variability inherent to these designs. Conventional epoching treats each event within a sequence as an independent response, discarding the temporal dependencies between successive events and obscuring systematic changes in neural state that accumulate across the sequence. In order to generate responses that capture the entire sequence, it necessitates alignment across trials to correct for the inherent temporal jitter that would otherwise blur averaged responses and obscure the true sequential dynamics. Existing temporal alignment methods warp observed signals directly, making them vulnerable to correlated noise and potentially disrupting multichannel temporal relationships essential for connectivity and causal analyses. Event-Related Warping (ERW) addresses these limitations by aligning template functions encoding experimental event structure rather than neural signals themselves. Templates constructed from event onsets and durations undergo smooth monotonic warping via gradient-based optimisation, then estimated trajectories are applied uniformly across all channels, preserving inter-channel timing relationships and causal structure. This design-level alignment exploits experimentally observable jitter whilst maintaining signal integrity. Simulations with known ground truth incorporating Gaussian jitter, skewed latencies, amplitude-latency coupling, and multi-parameter dependencies yielded standardised root-mean-square errors (sRMSE) of 0.27-0.38. Distance-weighted averaging, emphasising temporally consistent trials, provided 5-13% improvement when jitter exceeded 100 ms, with maximal benefit ({approx}13% reduction) under quadratic amplitude-latency coupling. Empirical validation using an auditory go/no-go dataset with cue-to-target intervals of 1.5-4.1 seconds demonstrated that ERW recovers jittered target-locked responses with comparable fidelity (sRMSE 0.24-0.51) to conventional epoching of time-locked events, whilst preserving inter-channel lag relationships (cross-covariance sRMSE 0.63-0.82). ERW thus extends standard trial averaging to scenarios where temporal variability would otherwise preclude coherent response recovery, supporting investigation of temporally extended processing in ecologically valid paradigms whilst maintaining compatibility with established ERP frameworks and downstream connectivity analyses.