diff --git a/response.txt b/response.txt new file mode 100644 index 0000000..cc4cf77 --- /dev/null +++ b/response.txt @@ -0,0 +1,26 @@ +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(ω∕2)² + y = cos(ω∕2)² + W = tan(ω0∕2)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