Magnitude Response of Basic Filters

• There are 4 main types of filters having amplitudes responses as shown below:
  

• Since no digital filter is ideal, they will always a have smooth (gradual) transition between the pass and stop bands:
  • the cutoff frequency $f_c$ is typically defined as the frequency at which the power transmitted drops by one half or 3 dB;
  • for pass-band filters, a quality factor $Q$ characterizes its bandwithdth BW:
    $$Q = \frac{f_c}{\mbox{BW}}.$$