Ideal filters and realizable filters

Section: Filtering
  • Ideal filter cut some frequencies while other are preserved. 4 types of filters:
  1. Low pass filter
  2. High pass filter
  3. Band pass filter
  4. Band cut filter

  • A filter is realizable iff its impulse response is stable and causal

  • Ideal filters are not realizable (not causal)

  • Two kind of realizable numerical filters:

  1. Finite Impulse Response (FIR) filters: $$ y[t] = \sum_{n=0}^{K-1} h[n]x[t-n] $$

  2. Infinite Impulse Response (IIR) filters $$ y[t] = \sum_{n=0}^{+\infty} h[n]x[t-n] $$