High-Pass Filter  Low-Pass Filter  Numerical Low-Pass Filter

High-Pass RC Filter:
•  
• Capacitor passes high frequencies, blocks low frequencies
• In frequency domain, capacitor impedance, Z(ω)=1/jωc
• So, the impulse response, 
• where,
• Whose magnitude,
• And phase,
• So that, 
• G is easiest viewed on a Bode (log-log) plot:
• Φ is 0° for high frequencies, 90° at low frequencies, and 45° at the -3dB point: 
• Note:  The affect of a high-pass filter can be numerically undone with the droop correction algorithm.

•  Low-Pass RC Filter:
  • Capacitor passes high frequencies, blocks low frequencies
  • In frequency domain, capacitor impedance, Z(ω)=1/jωc
  • So, the impulse response, 
  • where,
  • Whose magnitude,
  • And phase,
  • So that,
  • G is easiest viewed on a Bode (log-log) plot:
  • Φ is 0° for high frequencies, 90° at low frequencies, and 45° at the -3dB point: 

• Numerical Low-Pass RC Filter

  •  A simple algorithm can synthesize the response of input discrete-time waveform data to a low-pass RC filter.  A KCL node equation at the output node gives:

  • 

  • Or,

  • Which can be expressed by the implicit difference equation:

  • 

  • So,

  • where,

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