Recent high-density multi-electrode arrays pose new challenges for spike sorting in electrophysiology. In this work, we study online spike detection using concepts from sparse signal recovery. A linear convolutional model is used to describe the extracellular recording and compressed sensing is used to recover the spiking activity as a sparse signal. Error propagation in response to new measurements is characterized using results on banded matrices. We demonstrate that accurate signal recovery can be performed by processing finite buffers and derive improved buffer sizes, by introducing effective bandwidths. An adaptation of Compressive Sampling Matching Pursuit is proposed for online processing by restricting iterations to a finite buffer. Evaluation with noisy, ground-truth simulations show virtually identical performance to offline processing indicating an appropriate choice of the buffer size. Negligible errors were observed for signal-to-noise ratio larger than 7. Furthermore, the proposed online algorithm achieves spike detection comparable to manual spike sorting in high-density recordings from a behaving macaque (deviation: 6.6- 7.7%), while enabling resolution of overlapping activity. In summary we demonstrate that sparse signal recovery with limited buffer size enables accurate online spike detection. In combination with offline waveform extraction from training data, this provides a means for using single-neuron spiking activity in closed loop experiments or brain-machine interfaces.