The conversion of a normalized low-pass filter to a high-pass, band-pass, or band-stop filter type using the following substitutions for s in the normalized low-pass filter response transfer function (where s is the complex operator: see s-domain circuit analysis):
low-pass to high-pass: s → ωc/s
low-pass to band-pass: s → (s2 + ωc2)/Bs
low-pass to band-stop: s → Bs/(s2 + ωc2)
where ωc is the cut-off frequency and B is the bandwidth.