Methodology and Toolkit for Spectral Analysis of Neural Signals

We developed a toolkit that implements the algorithms to estimate the oscillatory bursts embedded in in vivo neural signals. The in vivo signals are decomposed into two components, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1/\mathrm{f}^{\beta}$</tex> background activity and the embedded oscillatory bursts. The bursts themselves can vary in amplitude, frequency, and number of cycles, making it challenging to characterize them. The first algorithm determines the statistical characteristics of the two components. The second one synthesizes each component individually using the estimated characteristics. The third algorithm captures the best integration of the two components using the Kullback-Leibler divergence criterion to generate an ‘in silico’ version of the in vivo local field potential (LFP) by matching its probability density function with that of the in vivo signal. The methodology and algorithms are illustrated using an in vivo dataset in the public domain. The software tool with the algorithms is available for public download.