Constants

•
• 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,