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Feature extraction, class and decomposition question

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decade5d

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what is actually a decomposition in signal ? what i get is that from a data of E(1) it goes to x(1)-x(n) composing that signal, where feature extraction is the act of extractng the data ? and class is when you get the data of the feature then it entered that classifier ? im still not very clear on this so please any help will be really appreciated
 

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