
Type : LPF 24dB/Oct
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
Added on : 28/07/06 by Christian[ AT ]savioursofsoul[ DOT ]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.
Added on : 15/10/06 by Christian[ AT ]savioursofsoul[ DOT ]de Comment : Just found out, that I forgot to remove the temporary variable 't'. It was used in my code for the speedup. You can simply ignore and delete it.
Added on : 13/02/09 by karatecoffee[ AT ]yahoo[ DOT ]dk Comment : Changing the frequency also seems to affect the volume quite a lot. That can't be right? Maybe you should repost this (and remove the "t" this time)? ;)
Added on : 13/02/13 by dj_zef[ AT ]ngs[ DOT ]ru Comment : Your filter does not work! Arise overload in the calculation of coefficients A and B in the cutoff frequency of approximately 10 khz. At low frequencies, the coefficient of the gain increases proportional to the frequency cutoff, which causes congestion. I also noticed that the filter on this basis, the package of ASIO/DSP  DDspBesselFilter.pas does not work, although Butterworth (DDspButterworthFilter.pas) and Chebyshev (DDspChebyshevFilter.pas) work perfectly!

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