For an expert cardiologist, any abnormality in the heart rhythm or electrocardiogram (ECG) shape can be easily detected as a sign of arrhythmia. However, this is a big challenge for a computer system. The need for automatic arrhythmia recognition comes from the development of many portable ECG measuring devices designed to function as a part of health monitoring platforms. These platforms, because of their wide availability, generate a lot of data and hence the need for algorithms to process this data. From the many methods for automatic heartbeat classification, convolutional neural networks (CNNs) are increasingly being applied in this ECG analysis task. The purpose of this paper is to develop arrhythmia classification model according to the standards defined by the Association for the Advancement of Medical Instruments (AAMI), using CNNs, on data from the publicly available MIT-BIH Arrhythmia database. We experiment with two types of heartbeat segmentation: static and dynamic. The ultimate goal is to implement an algorithm for long-term monitoring of a user's health, which is why we have focused on classification models from single-lead ECG, and, even more, on algorithms specifically designed for one person rather than general models. Therefore, we evaluate patient-specific CNN models also on measurements from a novel wireless single-lead ECG sensor.