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Modulation recognition finds its application in today's cognitive systems ranging from civilian to military installations. Existing modulation classification algorithms include classic likelihood approaches and feature-based approaches. In this study, approximate entropy, a nonlinear method to analyze a time series, is proposed as a unique characteristic of a modulation scheme. It is projected as a robust feature to identify signal parameters such as number of symbol levels, pulse lengths, and modulation indices of a continuous phase modulated (CPM) signal. The method is then extended to classify CPM signals with differing pulse shapes, which include raised cosine and Gaussian pulses with varying roll-off factors and bandwidth-time products, respectively. This approximate entropy feature-based approach results in high classification accuracies for a variety of signals and performs robustly even in the presence of synchronization errors and carrier phase offsets. Results are presented in the form of extensive simulations.