We designed and implemented a deep learning based RF signal classifier on the Field Programmable Gate Array (FPGA) of an embedded software-defined radio platform, DeepRadio, that classifies the signals received through the RF front end to different modulation types in real time and with low power. This classifier implementation successfully captures complex characteristics of wireless signals to serve critical applications in wireless security and communications systems such as identifying spoofing signals in signal authentication systems, detecting target emitters and jammers in electronic warfare (EW) applications, discriminating primary and secondary users in cognitive radio networks, interference hunting, and adaptive modulation. Empowered by low-power and low-latency embedded computing, the deep neural network runs directly on the FPGA fabric of DeepRadio, while maintaining classifier accuracy close to the software performance. We evaluated the performance when another SDR (USRP) transmits signals with different modulation types at different power levels and DeepRadio receives the signals and classifies them in real time on its FPGA. A smartphone with a mobile app is connected to DeepRadio to initiate the experiment and visualize the classification results. With real radio transmissions over the air, we show that the classifier implemented on DeepRadio achieves high accuracy with low latency (microsecond per sample) and low energy consumption (microJoule per sample), and this performance is not matched by other embedded platforms such as embedded graphics processing unit (GPU).