In comparison to the ideal low-pass, the RC low-pass lacks in the following characteristics:
The passband gain varies long before the corner frequency, fC, thus amplifying the
upper passband frequencies less than the lower passband.
The transition from the passband into the stopband is not sharp, but happens
gradually, moving the actual 80-dB roll off by 1.5 octaves above fC.
The phase response is not linear, thus increasing the amount of signal distortion
significantly.
The gain and phase response of a low-pass filter can be optimized to satisfy one of the
following three criteria:
1) A maximum passband flatness,
2) An immediate passband-to-stopband transition,
3) A linear phase response.
For that purpose, the transfer function must allow for complex poles
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