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Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT). Our proposed DCT-based harmonic blocks replace conventional convolutional layers to produce partially or fully harmonic versions of new or existing CNN architectures. Using DCT energy compaction properties, we demonstrate how the harmonic networks can be efficiently compressed by truncating high-frequency information in harmonic blocks thanks to the redundancies in the spectral domain. We report extensive experimental validation demonstrating benefits of the introduction of harmonic blocks into state-of-the-art CNN models in image classification, object detection and semantic segmentation applications.