Persistent homology (PH)–the conventional method in topological data analysis–is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic (\(\chi\))–a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On ECG5000, our single-feature ECS classifier achieves \(98\%\) accuracy with \(O(n+R\cdot T)\) complexity, compared with the \(62\%\) reported by a recent interpretability-focused PH-based method under closely matched protocol settings (same single-feature threshold-classifier setup and identical UCR train/test split); this remains a literature-based comparison rather than a fully reimplemented head-to-head benchmark. An AdaBoost extension raises accuracy to \(98.6\%\), comparable with deep learning results while retaining full interpretability. Strong results are also obtained on TwoLeadECG (\(94.1\%\)) and Epilepsy2 (\(92.6\%\)).
