This question is related to rough path theory. Consider we have obtained signature obtained from a set discrete data points postulating linear from one data point to another. Such signature are used in some machine learning applications. A link to such application is : https://sutdbrain.files.wordpress.com/2017/07/nengli_lim_sutd_technical_talk-first-half.pdf

I am looking for possibility of extracting information from the signature to construct the signal. This would similar to filtering as in digital signal processing https://en.wikipedia.org/wiki/Digital_signal_processing.

Are anyone aware of such application of signature? More importantly is there any model (in the literature) of the original discrete data points based on the linear (or other) combination of signature elements.

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    You need a more mathematical statement for your question, to make it interesting to mathematicians. It seems too broad. – kodlu Nov 27 at 3:52

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