Filter: 1-pole LPF
=== Transfer function ===
H(s) = 1/(s/w0 + 1)
H(z) = T*w0*(z + 1)/(T*w0*(z + 1) + 2*z - 2)
#pole = 1
=== Filter coeffients ===
b0 = T*w0/(T*w0 + 2)
b1 = T*w0/(T*w0 + 2)
a1 = (T*w0 - 2)/(T*w0 + 2)

Filter: 1-pole HPF
=== Transfer function ===
H(s) = s/(s + w0)
H(z) = 2*(z - 1)/(T*w0*(z + 1) + 2*z - 2)
#pole = 1
=== Filter coeffients ===
b0 = 2/(T*w0 + 2)
b1 = -2/(T*w0 + 2)
a1 = (T*w0 - 2)/(T*w0 + 2)

Filter: 2-pole LPF
=== Transfer function ===
H(s) = 1/(s**2/w0**2 + 1 + s/(Q*w0))
H(z) = Q*T**2*w0**2*(z + 1)**2/(Q*T**2*w0**2*(z + 1)**2 + 4*Q*(z - 1)**2 + 2*T*w0*(z - 1)*(z + 1))
#pole = 2
=== Filter coeffients ===
b0 = Q*T**2*w0**2/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
b1 = 2*Q*T**2*w0**2/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
b2 = Q*T**2*w0**2/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a1 = (2*Q*T**2*w0**2 - 8*Q)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a2 = (Q*T**2*w0**2 + 4*Q - 2*T*w0)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)

Filter: 2-pole HPF
=== Transfer function ===
H(s) = s**2/(w0**2*(s**2/w0**2 + 1 + s/(Q*w0)))
H(z) = 4*Q*(z - 1)**2/(Q*T**2*w0**2*(z + 1)**2 + 4*Q*(z - 1)**2 + 2*T*w0*(z - 1)*(z + 1))
#pole = 2
=== Filter coeffients ===
b0 = 4*Q/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
b1 = -8*Q/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
b2 = 4*Q/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a1 = (2*Q*T**2*w0**2 - 8*Q)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a2 = (Q*T**2*w0**2 + 4*Q - 2*T*w0)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)

Filter: 2-pole BPF
=== Transfer function ===
H(s) = s/(Q*w0*(s**2/w0**2 + 1 + s/(Q*w0)))
H(z) = 2*T*w0*(z - 1)*(z + 1)/(Q*T**2*w0**2*(z + 1)**2 + 4*Q*(z - 1)**2 + 2*T*w0*(z - 1)*(z + 1))
#pole = 2
=== Filter coeffients ===
b0 = 2*T*w0/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
b1 = 0
b2 = -2*T*w0/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a1 = (2*Q*T**2*w0**2 - 8*Q)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)
a2 = (Q*T**2*w0**2 + 4*Q - 2*T*w0)/(Q*T**2*w0**2 + 4*Q + 2*T*w0)