Convolutional Neural Networks (CNNs) specialize in feature extraction rather than function mapping. In doing so they form complex internal hierarchical feature representations, the complexity of which gradually increases with a corresponding increment in neural network depth. In this paper, we examine the feature extraction capabilities of CNNs using Maximum Entropy (ME) and Signal-to-Noise Ratio (SNR) to validate the idea that, CNN models should be tailored for a given task and complexity of the input data. SNR and ME measures are used as they can accurately determine in the input dataset, the relative amount of signal information to the random noise and the maximum amount of information respectively. We use two well known benchmarking datasets, MNIST and CIFAR-10 to examine the information extraction and abstraction capabilities of CNNs. Through our experiments, we examine convolutional feature extraction and abstraction capabilities in CNNs and show that the classification accuracy or performance of CNNs is greatly dependent on the amount, complexity and quality of the signal information present in the input data. Furthermore, we show the effect of information overflow and underflow on CNN classification accuracies. Our hypothesis is that the feature extraction and abstraction capabilities of convolutional layers are limited and therefore, CNN models should be tailored to the input data by using appropriately sized CNNs based on the SNR and ME measures of the input dataset.