Convolutional neural networks have often been proposed for processing radar Micro-Doppler signatures, most commonly with the goal of classifying the signals. The majority of works tend to disregard phase information from the complex time-frequency representation. Here, the utility of the phase information, as well as the optimal format of the Doppler-time input for a convolutional neural network, is analysed. It is found that the performance achieved by convolutional neural network classifiers is heavily influenced by the type of input representation, even across formats with equivalent information. Furthermore, it is demonstrated that the phase component of the Doppler-time representation contains rich information useful for classification and that unwrapping the phase in the temporal dimension can improve the results compared to a magnitude-only solution, improving accuracy from 0.920 to 0.938 on the tested human activity dataset. Further improvement of 0.947 is achieved by training a linear classifier on embeddings from multiple-formats.