Objective: To propose a novel deep neural network (DNN) architecture -- the filter bank convolutional neural network (FBCNN) -- to improve SSVEP classification in single-channel BCIs with small data lengths. Methods: We propose two models: the FBCNN-2D and the FBCNN-3D. The FBCNN-2D utilizes a filter bank to create sub-band components of the electroencephalography (EEG) signal, which it transforms using the fast Fourier transform (FFT) and analyzes with a 2D CNN. The FBCNN-3D utilizes the same filter bank, but it transforms the sub-band components into spectrograms via short-time Fourier transform (STFT), and analyzes them with a 3D CNN. We made use of transfer learning. To train the FBCNN-3D, we proposed a new technique, called inter-dimensional transfer learning, to transfer knowledge from a 2D DNN to a 3D DNN. Our BCI was conceived so as not to require calibration from the final user: therefore, the test subject data was separated from training and validation. Results: The mean test accuracy was 85.7% for the FBCCA-2D and 85% for the FBCCA-3D. Mean F1-Scores were 0.858 and 0.853. Alternative classification methods, SVM, FBCCA and a CNN, had mean accuracy of 79.2%, 80.1% and 81.4%, respectively. Conclusion: The FBCNNs surpassed traditional SSVEP classification methods in our simulated BCI, by a considerable margin (about 5% higher accuracy). Transfer learning and inter-dimensional transfer learning made training much faster and more predictable. Significance: We proposed a new and flexible type of DNN, which had a better performance than standard methods in SSVEP classification for portable and fast BCIs.