The Ideal Low-Pass Filter

• A low-pass filter is one that allows low frequencies to pass while attenuating anything above a specified cutoff frequency $f_c$:
  • pass band: the region where frequencies are permitted to pass;
  • stop band: the region where frequencies are attenuated.

• The amplitude response of an ideal low-pass filter:
  

• This ideal amplitude response is not realizable in discrete time; how close we come depends on the complexity of the filter.