RC Filters

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

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High-Pass RC Filter:

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   Capacitor passes high frequencies, blocks low frequencies

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

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Capacitor passes high frequencies, blocks low frequencies

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

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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:

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Or,

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Which can be expressed by the implicit difference equation:
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So,
where,       

  Raymond Allen 2006