independent Component Analysis: algorithms and applications: Difference between revisions
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==Motivation== | ==Motivation== | ||
Imagine a room where two people are speaking at the same time and two microphones are used to record the speech signals. Denoting the speech signals by <math>s_1(t) \,</math> and <math>s_2(t)\,</math> and the recorded signals by <math> x_1(t) \,</math> and <math>x_2(t) \,</math>, we | Imagine a room where two people are speaking at the same time and two microphones are used to record the speech signals. Denoting the speech signals by <math>s_1(t) \,</math> and <math>s_2(t)\,</math> and the recorded signals by <math> x_1(t) \,</math> and <math>x_2(t) \,</math>, we can assume the linear relation <math>x = As \,</math>, where <math>A \,</math> is a parameter matrix that depends on the distances of the microphones from the speakers. The interesting problem of estimating both <math>A\,</math> and <math>s\,</math> using only the recorded signals <math>x\,</math> is called the ''cocktail-party problem'', which is the signature problem for '''ICA'''. | ||
==Introduction== | ==Introduction== | ||
Revision as of 13:43, 5 July 2009
Motivation
Imagine a room where two people are speaking at the same time and two microphones are used to record the speech signals. Denoting the speech signals by [math]\displaystyle{ s_1(t) \, }[/math] and [math]\displaystyle{ s_2(t)\, }[/math] and the recorded signals by [math]\displaystyle{ x_1(t) \, }[/math] and [math]\displaystyle{ x_2(t) \, }[/math], we can assume the linear relation [math]\displaystyle{ x = As \, }[/math], where [math]\displaystyle{ A \, }[/math] is a parameter matrix that depends on the distances of the microphones from the speakers. The interesting problem of estimating both [math]\displaystyle{ A\, }[/math] and [math]\displaystyle{ s\, }[/math] using only the recorded signals [math]\displaystyle{ x\, }[/math] is called the cocktail-party problem, which is the signature problem for ICA.