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Existing datasets used to train deep learning models for narrowband radio frequency (RF) signal classification lack enough diversity in signal types and channel impairments to sufficiently assess model performance in the real world. We introduce the Sig53 dataset consisting of 5 million synthetically-generated samples from 53 different signal classes and expertly chosen impairments. We also introduce TorchSig, a signals processing machine learning toolkit that can be used to generate this dataset. TorchSig incorporates data handling principles that are common to the vision domain, and it is meant to serve as an open-source foundation for future signals machine learning research. Initial experiments using the Sig53 dataset are conducted using state of the art (SoTA) convolutional neural networks (ConvNets) and Transformers. These experiments reveal Transformers outperform ConvNets without the need for additional regularization or a ConvNet teacher, which is contrary to results from the vision domain. Additional experiments demonstrate that TorchSig's domain-specific data augmentations facilitate model training, which ultimately benefits model performance. Finally, TorchSig supports on-the-fly synthetic data creation at training time, thus enabling massive scale training sessions with virtually unlimited datasets.