This paper proposes a deep convolutional neural network for performing note-level instrument assignment. Given a polyphonic multi-instrumental music signal along with its ground truth or predicted notes, the objective is to assign an instrumental source for each note. This problem is addressed as a pitch-informed classification task where each note is analysed individually. We also propose to utilise several kernel shapes in the convolutional layers in order to facilitate learning of efficient timbre-discriminative feature maps. Experiments on the MusicNet dataset using 7 instrument classes show that our approach is able to achieve an average F-score of 0.904 when the original multi-pitch annotations are used as the pitch information for the system, and that it also excels if the note information is provided using third-party multi-pitch estimation algorithms. We also include ablation studies investigating the effects of the use of multiple kernel shapes and comparing different input representations for the audio and the note-related information.