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Say I have a data series of N elements.

I want to create second series that represents a rough approximation of the first series with a reduced set of elements M.

Question 1: Is there a proper name for the general set of techniques used to accomplish this?

Question 2: Is there a specific name for the following technique or similar techniques?

1 - Divide N / M, which produces a number of elements per bucket B.

2 - Calculate mean for first B elements. Calculate mean for second set of B elements.. so on and so forth.

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The word describing this process is called "downsampling". Sometimes referred to as "decimation".

Having come from a 3D background, I am familiar with reduction of points in a 3D mesh as "decimation". The terms seem to be used similarly in fields of computer graphics, communications, and economic analysis.

https://en.wikipedia.org/wiki/Downsampling_(signal_processing)

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