LPF 24dB/Oct

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First calculate the prewarped digital frequency:

K = tan(Pi * Frequency / Samplerate);

Now we calc some Coefficients:

sg = Sinh(PassbandRipple);
cg = Cosh(PassbandRipple);
cg *= cg;

Coeff[0] = 1 / (cg-0.85355339059327376220042218105097);
Coeff[1] = K * Coeff[0]*sg*1.847759065022573512256366378792;
Coeff[2] = 1 / (cg-0.14644660940672623779957781894758);
Coeff[3] = K * Coeff[2]*sg*0.76536686473017954345691996806;

K *= K; // (just to optimize it a little bit)

Calculate the first biquad:

A0 =   (Coeff[1]+K+Coeff[0]);
A1 = 2*(Coeff[0]-K)*t;
A2 =   (Coeff[1]-K-Coeff[0])*t;
B0 = t*K;
B1 = 2*B0;
B2 = B0;

Calculate the second biquad:

A3 =   (Coeff[3]+K+Coeff[2]);
A4 = 2*(Coeff[2]-K)*t;
A5 =   (Coeff[3]-K-Coeff[2])*t;
B3 = t*K;
B4 = 2*B3;
B5 = B3;

Then calculate the output as follows:

Stage1 = B0*Input + State0;
State0 = B1*Input + A1/A0*Stage1 + State1;
State1 = B2*Input + A2/A0*Stage1;

Output = B3*Stage1 + State2;
State2 = B4*Stage1 + A4/A3*Output + State2;
State3 = B5*Stage1 + A5/A3*Output;

Comments

You've used two notations here (as admitted on KVR!)..
Updated calculation code reads:

=-=-=-= Start =-=-=-=

Calculate the first biquad:

//A0 =   (Coeff[1]+K+Coeff[0]);
t  = 1/(Coeff[1]+K+Coeff[0]);
A1 = 2*(Coeff[0]-K)*t;
A2 =   (Coeff[1]-K-Coeff[0])*t;
B0 = t*K;
B1 = 2*B0;
B2 = B0;

Calculate the second biquad:

//A3 =   (Coeff[3]+K+Coeff[2]);
t  = 1/(Coeff[3]+K+Coeff[2]);
A4 = 2*(Coeff[2]-K)*t;
A5 =   (Coeff[3]-K-Coeff[2])*t;
B3 = t*K;
B4 = 2*B3;
B5 = B3;

Then calculate the output as follows:

Stage1 = B0*Input + State0;
State0 = B1*Input + A1*Stage1 + State1;
State1 = B2*Input + A2*Stage1;

Output = B3*Stage1 + State2;
State2 = B4*Stage1 + A4*Output + State2;
State3 = B5*Stage1 + A5*Output;

=-=-=-=  End  =-=-=-=

Hope that clears up any confusion for future readers :-)

The variable State3 is assigned a value, but is never used anywhere. Is there a reason for this?

Just ported this into Reaper's native JesuSonic.

There are errors in both of the codes above :D
Use this:

//start

A0  = 1/(Coeff[1]+K+Coeff[0]);
A1 = 2*(Coeff[0]-K)*A0;
A2 = (Coeff[1]-K-Coeff[0])*A0;
B0 = A0*K;
B1 = 2*B0;
B2 = B0;

A3  = 1/(Coeff[3]+K+Coeff[2]);
A4 = 2*(Coeff[2]-K)*A3;
A5 = (Coeff[3]-K-Coeff[2])*A3;
B3 = A3*K;
B4 = 2*B3;
B5 = B3;

Stage1 = B0*Input + State0;
State0 = B1*Input + A1*Stage1 + State1;
State1 = B2*Input + A2*Stage1;
Output = B3*Stage1 + State2;
State2 = B4*Stage1 + A4*Output + State3;
State3 = B5*Stage1 + A5*Output;

//end

@RossClement[ AT ]gmail[ DOT ]com
'State3' should be added in this line
-> State2 = B4*Stage1 + A4*Output + State3;