In this paper, we examine the use of a deep multi-layer perceptron architecture to classify received signals as one of seven common waveforms, single carrier (SC), single-carrier frequency division multiple access (SC-FDMA), orthogonal frequency division multiplexing (OFDM), linear frequency modulation (LFM), amplitude modulation (AM), frequency modulation (FM), and phase-coded pulse modulation used in communication and radar networks. Synchronization of the signals is not needed as we assume there is an unknown and uncompensated time and frequency offset. The classifier is open-set meaning it assumes unknown waveforms may appear. Isolation forest (IF) models acting as binary classifiers are used for each known signal class to perform detection of possible unknown signals. This is accomplished using the 32-length feature vector from a dense layer as input to the IF models. The classifier and IF models work together to monitor the spectrum and identify waveforms along with detecting unknown waveforms. Results showed the classifier had 100% classification rate above 0 dB with an accuracy of 83.2% and 94.7% at -10 dB and -5 dB, respectively, with signal impairments present. Results for the IF models showed an overall accuracy of 98% when detecting known and unknown signals with signal impairments present. IF models were able to reject all unknown signals while signals similar to known signals were able to pass through 2% of the time due to the contamination rate used during training. Overall, the entire system can classify correctly in an open-set mode with 98% accuracy at SNR greater than 0 dB.