Synthetic multimedia contents created through AI technologies, such as Generative Adversarial Networks (GAN), applied to human faces can have serious social and political consequences. State-of-the-art algorithms employ deep neural networks to detect fake contents but, unfortunately, almost all approaches appear to be neither generalizable nor explainable. In this paper, a new fast detection method able to discriminate Deepfake images with high precision is proposed. By employing Discrete Cosine Transform (DCT), anomalous frequencies in real and Deepfake image datasets were analyzed. The \beta statistics inferred by the distribution of AC coefficients have been the key to recognize GAN-engine generated images. The proposed technique has been validated on pristine high quality images of faces synthesized by different GAN architectures. Experiments carried out show that the method is innovative, exceeds the state-of-the-art and also gives many insights in terms of explainability.