Accelerated acquisition of long-term and longitudinal signals has motivated new approaches for processing and analysis. Topological data analysis (TDA) has recently been proposed for analyzing these large and complex data. TDA provides significant insight through coarse, global structures, while maintaining the local structure of measurements. TDA visualizations enhance its interpretive power. However, TDA recovers structure only with a judicious choice of parameters. In this paper, a method for analyzing time series involving a time-delay lift of that signal to a higher dimension is proposed, wherein useful information is obtained by considering lifts across a range of time delays. Applied to ECG records, TDA visualizations uncover ectopic and other abnormal occurrences in long signals. The results indicate a promising direction for providing further insights into complex time series, particularly for longitudinal physiological signals.