System

Linear Time/Translation Invariant (LTI) Operators (Chap.

22.1)

  1. e-function: \( \tilde{e}_f(t) = e^{i2\pi ft} \)
  2. \( G(f) = \mathcal{F}{ g(t) } \)
  3. stable: bounded input produces bounded output
  4. Given \( \mathbb{H} \) is LTI. Stable is equivalent to \( h(t) \) absolutely integrable.
  5. Given \( \mathbb{H} \) is LTI. Causal is equivalent to \( h(t)=0, \forall t<0 \).

Circulant Matrix

e-functions and DFT

Characterization

🏷 Category=Probability