Brain research is concerned with two types of electrophysiological signals: neural action potentials (AP), which are also known as spikes, and local field potentials (LFP). The demand for an increased spatial and temporal resolution leads to an enlarged data rate which has to be handled by an assumed wireless link between the signal sources and the base station. Without data compression, these data rates would conflicting the neurophysiological restrictions in terms of low energy and low area consumption. The theory of Compressed Sensing (CS) can be utilized to perform data compression right after or during the acquisition of the neural data. In order to apply a joint CS infrastructure to AP and LFP, a common basis in which both signal types can be characterized as sufficiently sparse has to be found. In this paper, we investigate and compare four different well-known bases for the joint compression of LFP and AP of which the discrete cosine transform (DCT) turns out to be best suited.