visualize PT(N) as butterworth

[nerdCopter]

Pull-Request #59

--butterworth commandline parameter required.

What is Butterworth Correction?

When cascading multiple PT1 (single-pole) filters to create a higher-order PTn filter (PT2, PT3, etc.), the combined filter does not naturally have its -3dB cutoff at the configured frequency. To achieve a true Butterworth response (flat passband, -3dB at cutoff), each stage must be set to a higher cutoff frequency.

Correction formula:

PTn cutoff correction = 1 / sqrt(2^(1/n) - 1)

• PT1: 1.0× (no correction)
• PT2: 1.554×
• PT3: 1.961×
• PT4: 2.298×