• In general, low-pass filter kernels are composed of a group of adjacent positive points. This results in each sample in the output signal being a weighted average of many adjacent points from the input signal. This averaging smoothes the signal, thereby removing high-frequency components.
  • If a low-pass filter has a gain of one at DC (zero frequency), then the sum of all of the points in the impulse response must be equal to one.
  • Passive Filter
    • cut-off point
      • the frequency where high or low-frequencies will be removed
    • slope
      • decibels per octave
      • describes a ratio of how the filter attenuates frequencies past the cut-off point
  • Active Filter
\begin{align} i_o=g_m v_1,v_o=\frac{1}{C}\int i_o dt,v_o=\frac{g_m}{C}\int v_1 dt \end{align}
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