A practical guide for digital IIR audio filters has cookbook-style values for creating higher-order Bessel filters out of biquads, but the values listed aren't very precise:
You should multiply the Fc for each stage by the following coefficients:
1: 1.00
2: 1.27
3: 1.32 1.45
4: 1.60 1.43
5: 1.50 1.76 1.56
6: 1.90 1.69 1.60
The corresponding Q values are:
1: ---
2: 0.58
3: --- 0.69
4: 0.81 0.52
5: ---- 0.92 0.56
6: 1.02 0.61 0.51
What are the expressions to calculate these values exactly?
For the Butterworth table, the values are given by Q = 1/(2 * sin((pi / N) * (n + 1 / 2)))
, for instance. So where the table says 4: 0.54 1.31
, the equation gives 1.3065629648763766 and 0.54119610014619701. But I can't find the expression for Bessel filters, except that 2: 0.58
is $1\over\sqrt3$.
Prototype-generating functions just have long tables of numbers, so maybe these are not easy to calculate? (Bessel functions?) If so, a listing of these Q and Fc values for the first several orders would be good.
(And yes, I know the bilinear transformed Bessel is no longer linear-phase. :/ I just want to know where these numbers are from.)