Capturing audio signals with specific directivity patterns is essential in speech communication. This study presents a deep neural network (DNN)-based approach to directional filtering, alleviating the need for explicit signal models. More specifically, our proposed method uses a DNN to estimate a single-channel complex mask from the signals of a microphone array. This mask is then applied to a reference microphone to render a signal that exhibits a desired directivity pattern. We investigate the training dataset composition and its effect on the directivity realized by the DNN during inference. Using a relatively small DNN, the proposed method is found to approximate the desired directivity pattern closely. Additionally, it allows for the realization of higher-order directivity patterns using a small number of microphones, which is a difficult task for linear and parametric directional filtering.