Re:Hilbert space: treating functions as vectors
by defmacr0 on Friday November 21, 2025 @05:20AM
(#46003094)
Fwiw, my favourite textbook in communication theory (Lapidoth, A Foundation in Digital Communication) explicitly calls out this issue of working with equivalence classes of signals and chooses to derive most theorems using the tools available when working in ℒ_2 (square-integrable functions) and ℒ_1 space
If you want to talk about applications, then this representation is especially bad. Since the intuition it gives is just straight up false.