The information processing in the brain is governed by large neural ensembles organized in networks. The firing of the neuronal cells in each neural population bring insight on the role of this structure for a given task or on its involvement in a pathology. Such investigations require the detection and sorting of neuronal spikes from the recordings. This is known as a challenging task due to the high level of surrounding local field potential (LFP) and to the strong similarities between the patterns to classify. In this article we present a new method for spike classification leaning on the separation between the spike waveform and the background LFP. The approach is rooted in a Bayesian framework integrating prior on the LFP spectral density and considering mixture of Gaussian for the classification. The algorithm provides both the posterior mean of the spike waveforms for each cluster as well as the posterior mean of each singular spike waveforms.