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Question for anyone reading the paper; what exactly is the notation in these two stages below supposed to mean? 𝑦(𝑡) = Ch(𝑡) (1b) 𝑦𝑡 = Ch𝑡 (2b) This

Question for anyone reading the paper; what exactly is the notation in these two stages below supposed to mean? 𝑦(𝑡) = Ch(𝑡) (1b) 𝑦𝑡 = Ch𝑡 (2b) This is from the section describing state space models. The paragraphs before seem to describe e.g. 𝑦(𝑡) as being presumably the real value element in function/sequence 𝑦 evaluated at time 𝑡. However, it then randomly adds the 𝑦𝑡 (note the 𝑡 is supposed to be subscript) notation for what looks to be a similar equivalence and I’m not sure how thats supposed to differ in meaning from 𝑦(𝑡). Am I dumb?

molticrystal 3y ago
y(t) is likely continuous and y_t , the subscript form, is likely the discrete version. For example it is common in digital devices to sample something continuous(analog) every unit of time and use whatever value was captured at that moment for whatever the goal is, ideally if the something is sampled frequently enough you can even recreate the continuous version from the values.
- malwrar 3y ago
  Thanks for clarifying that! I think this makes sense, I wish I had a stronger math background so that this kind of thing doesn’t trip me up as much.
wenc 3y ago
As the other comment suggested, it's the discrete subscript. Normally t is notation for continuous time, and k the discrete time subscript, but all this is just convention. yₖ = Chₖ