We developed a generalized technique to characterize polymer-nanopore interactions via single channel ionic current measurements. Physical interactions between analytes, such as DNA, proteins, or synthetic polymers, and a nanopore cause multiple discrete states in the current. We modeled the transitions of the current to individual states with an equivalent electrical circuit, which allowed us to describe the system response. This enabled the estimation of short-lived states that are presently not characterized by existing analysis techniques. Our approach considerably improves the range and resolution of single-molecule characterization with nanopores. For example, we characterized the residence times of synthetic polymers that are three times shorter than those estimated with existing algorithms. Because the molecule's residence time follows an exponential distribution, we recover nearly 20-fold more events per unit time that can be used for analysis. Furthermore, the measurement range was extended from 11 monomers to as few as 8. Finally, we applied this technique to recover a known sequence of single-stranded DNA from previously published ion channel recordings, identifying discrete current states with subpicoampere resolution.