gists/response.txt

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if you have a transfer function like,
b2·s² + b1·s + b0
H(s) = ———————————————————
a2·s² + a1·s + a0
whereas s would be (1 - z⁻¹)(1 + z⁻¹)e^(j·ω) in the bilinear transform,
you can find its magnitude response with this equation:
(b2·x)² - (2·b2·b0 - b1²)·W·x·y + (b0·W·y)²
|H(j·ω)|² = —————————————————————————————————————————————
(a2·x)² - (2·a2·a0 - a1²)·W·x·y + (a0·W·y)²
(analog) x = ω²
y = 1
W = ω0²
(digital) x = sin(ω2)²
y = cos(ω2)²
W = tan(ω02)²
whereas ω is the physical frequency in rads/sec
ω0 is the center frequency in rads/sec
and the phase? maybe some other time
note: I'm no math genius and there's probably an error in here