Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. In contrast, in this paper we propose harmonic blocks that produce features by learning optimal combinations of responses to preset spectral filters. We rely on the use of the Discrete Cosine Transform filters which have excellent energy compaction properties and are widely used for image compression. The proposed harmonic blocks are intended to replace conventional convolutional layers to produce partially or fully harmonic versions of new or existing CNN architectures. We demonstrate how the harmonic networks can be efficiently compressed by exploiting redundancy in spectral domain and truncating high-frequency information. We extensively validate our approach and show that the introduction of harmonic blocks into state-of-the-art CNN models results in improved classification performance on CIFAR and ImageNet datasets.