Directed Transfer Function: A Pioneering Concept in Connectivity Analysis
Over the last half century, neuroscience largely concentrated itself on the problems of localization of brain centers connected with recognition of a given stimulus or with a given behavior. Besides anatomical studies, different imaging methods based mainly on the metabolism changes in brain were developed. The problem of identification of the brain activity sources was approached by means of varied inverse problem solutions. However, understanding brain information processing requires identification of the causal relations between active centers. To this aim, methods for estimation of causal influence that one system exerts another were developed. During the last 10 years, the problem of functional connectivity became a focus of attention in brain research. Here, we describe the development of methods, which
became valuable tools for estimation of the transmission between brain structures and, in particular, for the assessment of dynamic information processing by the brain.
In spectral analysis, we consider the properties of the signals in the frequency domain and the basic measure is the power spectral density (or power spectrum) describing the frequency content of a signal. There are various approaches for estimation of the power spectrum. In general, we can divide these methods into two groups: nonparametric and parametric. Nonparametric methods derive spectral quantities directly from the signal values. The Fourier transform is a nonparametric method that is very popular in every field of data analysis. This simple and straightforward implementation method makes one assumption about the signal, namely, that an infinite or periodic signal can be represented by a certain number of sinusoids. There exists a fast and effective algorithm for its estimation called FFT (fast Fourier transform).