musicdsp.org source code archive - WSInf

Type : LPF 24dB/Oct (click this to go back to the index)
Type : Bessel Lowpass
References : Posted by Christian[AT]savioursofsoul[DOT]de
Notes :
The filter tends to be unsable for low frequencies in the way, that it seems to flutter, but it never explode. At least here it doesn't.
Code :
First calculate the prewarped digital frequency:
K = tan(Pi * Frequency / Samplerate);
K2 = K*K; // speed improvement
Then calc the digital filter coefficients:
A0 = ((((105*K + 105)*K + 45)*K + 10)*K + 1);
A1 = -( ((420*K + 210)*K2 - 20)*K - 4)*t;
A2 = -( (630*K2 - 90)*K2 + 6)*t;
A3 = -( ((420*K - 210)*K2 + 20)*K - 4)*t;
A4 = -((((105*K - 105)*K + 45)*K - 10)*K + 1)*t;
B0 = 105*K2*K2;
B1 = 420*K2*K2;
B2 = 630*K2*K2;
B3 = 420*K2*K2;
B4 = 105*K2*K2;
Per sample calculate:
Output = B0*Input + State0;
State0 = B1*Input + A1/A0*Output + State1;
State1 = B2*Input + A2/A0*Output + State2;
State2 = B3*Input + A3/A0*Output + State3;
State3 = B4*Input + A4/A0*Output;
For high speed substitude A1/A0 with A1' = A1/A0...
Comments
from : Christian@savioursofsoul.de
comment : It turns out, that the filter is only unstable if the coefficient/state precision isn't high enough. Using double instead of single precision
already makes it a lot more stable.