Heart arrhytmias are rhythm disorders, which affects the heart and can lead to stroke, hospitalization, and a lower quality of life. Arrhythmias are often detected and diagnosed by using an electrocardiogram (ECG) and in many cases, the early detection of an arrhythmia can greatly increase the chance of a better recovery. The goal of this project is to develop a prototype of a portable ECG-system which can record and classify ECG-signals in real-time so that arrhythmias can be detected as early as possible. The prototype is made up of 1) a wireless ECG measurement unit consisting of a micro-controller, electrodes, an analog front-end, and a Bluetooth module, to capture ECG-signals from a person and transmit them via Bluetooth to a smartphone; and 2) an application implemented on a smartphone that is used to record/receive, visualize and classify ECG-signals. The classification is performed using a machine learning technique - a modular convolutional neural network, which is developed and trained by using a data set of ECG-signal features that is based on R-peaks. The prototype has been developed and tested. The test results have shown that the prototype is fully functional in terms of ECG-signal acquisition, transmission and classification. The results of evaluating the classifier show a weighted average recall of 98%, and a weighted average precision of 98%. The smart phone application used to record and classify the ECG-signals is shown to have a small footprint on the energy consumption of the smartphone, allowing for lengthy recordings. The performance of the classifier can be further improved through the use of a larger and more balanced data set.