Order: 3
ωc = 0.5π
Linear Scale
Maximally flat magnitude response in the passband
Maximally Flat: The Butterworth filter has the flattest possible passband response - all derivatives of the magnitude response are zero at ω = 0.
Roll-off: The attenuation is -20n dB/decade (or -6n dB/octave) where n is the filter order.
Pole Locations: Poles are equally spaced on the left half of a circle of radius ωc in the s-plane, ensuring stability.
At Cutoff: The magnitude is always -3 dB (≈ 0.707) at the cutoff frequency, regardless of order.
Trade-off: Higher order = sharper transition but more phase distortion and complexity.