As the use of wireless communication expands demand for radio spectrum, so does the need for effective automatic modulation recognition (AMR). Current methods of AMR include feature extractions, maximum likelihood algorithms, and deep learning (DL) networks primarily based on CNN structures. Many methods are limited by the slow training and testing time, the need for massive amounts of training data, and low probability of correct classification in the presence of noise. Our research proposes using a fully connected dense network instead of a convolutional one to mitigate some of these challenges. To test modulation classification accuracy, we used in-phase and quadrature samples from data sets at various signal-to-noise levels to evaluate 5 DL networks and a matched filter approach. Our experiments show that compared to traditional convolutional networks, our fully connected network improves training and testing times by order of magnitude, has an accuracy within 5% of the most accurate convolutional network, and uses a factor of 32 fewer parameters. We also demonstrate that using a bank of matched filters remains challenging, as correctly discriminating amongst several positive matches is not straightforward.