Improved optimal linear filters for the discrimination of multichannel waveform templates for spike-sorting applications

Optimal linear filters are well known as a useful technique for processing extracellular recordings of neural activity. They can be tuned to respond only to a corresponding waveform template, while minimizing the energy of all other templates, and can be used to resolve spikes that are overlapping. The derivation of optimal linear multichannel filters goes back to , but the computation is usually carried out in the frequency domain. This procedure, however, may introduce artefacts, because it assumes a cyclic cross correlation as the filtering operation, which is not applicable for filtering long signals. The only way to avoid the problems of cyclic operations is zero padding, at the expense of longer filters and, hence, higher filtering costs. In this letter, we propose to derive the optimal linear multichannel filters in the time domain, using the correct noncyclic operations. This leads to a quadratic optimization problem with linear constraints and allows us to formulate the filters as a function of the waveform templates in closed form. We compare the quality of the time-domain derived filters to those derived in the frequency domain in terms of their responses to waveform templates, which we extracted from real tetrode recordings. It turns out that the time-domain filters never perform worse than the frequency-domain filters but can be significantly shorter with the same or better performance.