Methods for studying the neural basis of voluntary behavior, part II: wavelet decompositions and other joint time-frequency analyses of local field potentials

Changes in a cell\´s spike rate are the outcome of pre-processing occurring in its thousands of dendro-dendritic and dendro-axonal synapses. In this paper we describe a sequence of analytic steps, including a novel use of the continuous wavelet transform, that we have developed for studying the synaptic pre-processing accompanying behaviorally significant spike rate variance seen in our movement tasks. Synaptic membrane activity is highly nonstationary, which poses difficulties for traditional spectral techniques such as Fourier analysis because of the frequency-time compromises inherent in such techniques. Thus, we apply multiple joint time-frequency techniques to our LFP data to visualize distributions of energy at different frequencies across task-time. First we segment the task into behavioral phases associated with significant co-modulation of spike rate and LFP amplitude fluctuations on single trials. Next we use coherence analyses to select representative LFPs from each area, and select a so-called mother wavelet for the continuous wavelet transform, yielding a time resolution at the millisecond scale. The mother wavelet is chosen for its proven biological plausibility and its ability to allow complete LFP reconstruction. Because of its partially redundant representation of energy across frequency and time, the continuous wavelet transform is particularly suitable for visualizing the task\´s "time-frequency topology". We then cross-validate these results by performing orthogonal versus non-orthogonal wavelet transforms and other JTFAs such as Gabor and short-time Fourier analyses. Finally, we use the discrete wavelet transform to combine data for a given task across trials, and test for non-background distribution of energy across frequency and time with chi-squared analyses.