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We know that moments extract important features of a signal that has no redundancy. For example Zernike moment gives us rotation invariant data of a signal like image or Fourier gives us frequency of a signal to us.

  • But what is the theory behind it?
  • How a moment performs this?
  • How basis function of a moment is designed?

I think it has roots in many different math theory but I can't find out a good source to know.

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    $\begingroup$ Your question is too broad – can you define what a moment is here, and how it differs from what you find in the wikipedia article or what you don't understand of that article? $\endgroup$ – Marcus Müller Jan 7 '17 at 15:15
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I dont think there is a common framework for defining all those operators. Each of them were developed by different people, at several moments of the history. They are being integrated day by day onto a common discipline called DSP.

As clarification, an operator (like a moment or any other) and the "redundancy" of a signal are very different and unrelated concepts.

IF you want a deeper answer, list all the moments you are considering, and all the different math theories you are reviewing for each of them.

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