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So a 1D mean filter of size two with a sliding window defined as W below could be considered as having a stride of one.

Wn=(Xn + Xn+1) / 2

Vn=W2n

where as if I were to define a 1D 'stepped mean filter' with a stride of two and labeled U below.

Un= (X2n + X2n+1) / 2

where the number of samples in U (and also V) would be half that of W.

My questions are the following

  1. Is U still a filter (I'm guessing it is even though not fitting with the traditional kernel convolution implementation I associate with filters)
  2. What is the technical language one could use to communicate and research questions regarding filter/non-filter such as just given?
  3. All though not directly related but since I have the floor is, if V and U would produce equivalent results (my intuition says no)?
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    $\begingroup$ Google “multirate filters” “multirate signal processing” $\endgroup$ – Stanley Pawlukiewicz Oct 16 at 14:56
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That's a decimating filter. As such, it serves as a 1/2-rate resampler.

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