Signal Processing Approach

• Every linear differential equation (with constant coefficients) gives rise to a linear, time-invariant (LTI) ``network'' or ``medium''
• LTI media are characterized by their frequency response $H(e^{j\omega})$ which breaks down into
  • Attenuation versus frequency:
    $$G(\omega) = \left\vert H(e^{j\omega})\right\vert$$

  • Time-delay versus frequency:
    $$P(\omega) = -\angle H(e^{j\omega})/\omega$$

  for each input-output pair
• Typical Procedure: Design an optimal digital filter to give desired frequency response
• In multi-input, multi-output cases, a matrix frequency response applies
• Often the filter structure can be chosen to maintain a physical interpretation of all state variables