We describe a cognitive system for recognizing and classifying radio signals by modulation type with various signal-to-noise ratios. System components include an ensemble of convolutional neural network (CNN) machine learning models, wavelet compressive sensing, and an optimization function. The chosen deep learning network model per signal is validated using a DeepSig data set consisting of 24 digital and analog modulation over the air recordings. Given a large amount of signal truth data, a model is trained to recognize features of differing modulation types using different supervised gradient learning algorithms with CNN based classification. The models, when applied to unseen signals, estimate a preliminary modulation based on a learned feature set. Multiple models are created and trained end-to-end and the best model and results are determined. We use linear programming optimization to determine the best model from an ensemble of classification models.  With increasing growth of technology, there is a higher demand to compress, handle, and encode more information using fewer bits. Digital information must be stored and retrieved in a highly efficient and effective manner while reducing the data redundancy to save hardware space and transmission time. The Discrete Wavelet Transform (DWT) provides a mathematical method of encoding information in such a way that it is layered according to level of detail. This layering produces approximations and details at various intermediate stages and facilitates less storage space than the original signal data. We use a complex 1D signal compression method, using the Haar wavelet with perfect reconstruction, as the basis function. The effect of deep learning classification using wavelet compressive sensing for signal classification is quantitatively shown with accuracy performance curves. Our approach results in higher accuracy and precision when compared with individual machine learning algorithms alone.