The advancements of wireless body area networks (WBAN) and wireless personal area networks (WPAN) has led to a recent increase of viable applications in wireless medical and healthcare devices. Developing biomedical sensors such as electroencephalograph (EEG) and electrocardiogram (ECG) sensors often require nnmerous connecting wires which may introduce noise and increase patient discomfort. In this paper we propose a system design and realization of a wireless EEG and ECG sensor network focusing on issues such as time synchronization, bandwidth, and power constraints constituent of WBANs. Our WSN comprises three transmitting nodes for a total of four EEG channels and an ECG channel. We solve problems such as data throughput requirements for EEG and ECG signal processing as well as time synchronization of received data at the base station. This paper keeps in consideration the possible implementation of our proposed system onto a system-on-chip (SOC) by puffing focus on the chip size and low power consumption of the analog-front-end system.