Building higher order filters with Biquads

The standard filters in CamillaDSP are not of a specific type, like Butterworth. Instead they are generic, with an adjustable q-value. To make the normal filters, one or several generic filters have to be used together.

Bessel

Making a Bessel filter with a set of Biquads requires creating several Biquads, each with a unique Q and cut-off frequency.

Multiplication factor for frequency:

The asterisk (*) indicates that this is a 1st order filter.

Q values:

Example Bessel filter

Let’s make a 5th order Lowpass at 1 kHz. Loking at the tables we see that we need three filters. The first should be a 1st order while the second and third are 2nd order.

• First filter, type LowpassFO:
  • freq = 1kHz * 1.50231627145 = 1502Hz
  • (no q-value)
• Second filter, type Lowpass:
  • freq = 1kHz * 1.75537777664 = 1755Hz
  • q = 0.916477373948
• Third filter, type Lowpass:
  • freq = 1kHz * 1.5563471223 = 1556Hz
  • q = 0.563535620851

Butterworth and Linkwitz-Riley

For an Nth order Butterworth you will have N/2 biquad sections if N is even, and ((N+1)/2 if N is odd. For odd filters one of the Biquads will be a first order filter. Each filter will have the same resonant frequency f0 and the second order filters will have Q according to this formula:

Q = 1/( 2*sin((pi/N)*(n + 1/2)) )

where 0 <= n < (N-1)/2

Table for q-values

Butterworth and Linkwitz-Riley filtes can easily be built with Biquads. The following table lists the most common ones. High- and lowpass use the same parameters.

Note that a 4th order LR iconsists of two 2nd order Butterworth filters, and that an 8th order LR consists of two 4:th order Butterworth filters.