This paper focuses on Discrete-Time Cellular Neural Networks (DTCNNs) for associative memories with application to pattern classification. At first, DTCNNs with a globally asymptotically stable equilibrium point are designed to behave as associative memories. The objective is achieved by considering feedback parameters related to circulant matrices and by satisfying frequency domain stability criteria. The approach, by generating DTCNNs where the input data are fed via external inputs rather than initial conditions, enables both hetero-associative and auto-associative memories to be designed. Numerical examples are reported in order to show the capabilities of the design tool. Successively, an application of DTCNNs to pattern classification is illustrated. Namely, it is shown that patterns belonging to the training set as well as patterns outside it can be reliably classified using the proposed design method. Comparisons with well-established classification techniques, such as signature technique and modified Fourier descriptor technique, clearly highlight the performances of the approach developed herein.