**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[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.

__from__ : 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.

__from__ : 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 re-post this (and remove the "t" this time)? ;)

__from__ : 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!