Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited heart muscle disease that appears between the second and forth decade of a patient's life, being responsible for 20% of sudden cardiac deaths before the age of 35. The effective and punctual diagnosis of this disease based on Electrocardiograms (ECGs) could have a vital role in reducing premature cardiovascular mortality. In our analysis, we firstly outline the digitalization process of paper-based ECG signals enhanced by a spatial filter aiming to eliminate dark regions in the dataset's images that do not correspond to ECG waveform, producing undesirable noise. Next, we propose the utilization of a low-complexity convolutional neural network for the detection of an arrhythmogenic heart disease, that has not been studied through the usage of deep learning methodology to date, achieving high classification accuracy on a disease the major identification criterion of which are infinitesimal millivolt variations in the ECG's morphology, in contrast with other arrhythmogenic abnormalities. Finally, by performing spectral analysis we investigate significant differentiations in the field of frequencies between normal ECGs and ECGs corresponding to patients suffering from ARVC. The overall research carried out in this article highlights the importance of integrating mathematical methods into the examination and effective diagnosis of various diseases, aiming to a substantial contribution to their successful treatment.