Editing Signal separation (section)

== Mathematical representation ==
[[File:BSS-flow-chart.png|thumb|Basic flowchart of BSS]]
The set of individual source signals, <math>s(t) = (s_1(t), \dots, s_n(t))^T</math>, is 'mixed' using a matrix, <math>A=[a_{ij}] \in \mathbb{R}^{m \times n}</math>, to produce a set of 'mixed' signals, <math> x(t)=(x_1(t), \dots, x_m(t))^T </math>, as follows.  Usually, <math>n</math> is equal to <math>m</math>. If <math>m > n</math>, then the system of equations is overdetermined and thus can be unmixed using a conventional linear method. If <math>n > m</math>, the system is underdetermined and a non-linear method must be employed to recover the unmixed signals. The signals themselves can be multidimensional.

<math>x(t) = A\cdot s(t)</math>

The above equation is effectively 'inverted' as follows. Blind source separation separates the set of mixed signals, <math> x(t) </math>, through the determination of an 'unmixing' matrix, <math>B = [B_{ij}] \in \mathbb{R}^{n \times m}</math>, to 'recover' an approximation of the original signals, <math> y(t) = (y_1(t), \dots, y_n(t))^T</math>.<ref>Jean-Francois Cardoso “Blind Signal Separation: statistical Principles” http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.462.9738&rep=rep1&type=pdf</ref><ref>Rui Li, Hongwei Li, and Fasong Wang. “Dependent Component Analysis: Concepts and Main Algorithms” http://www.jcomputers.us/vol5/jcp0504-13.pdf</ref><ref name=":0">Aapo Hyvarinen, Juha Karhunen, and Erkki Oja. “Independent Component Analysis” https://www.cs.helsinki.fi/u/ahyvarin/papers/bookfinal_ICA.pdf pp. 147–148, pp. 410–411, pp. 441–442, p. 448</ref>

<math>y(t) = B\cdot x(t)</math>