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Direct Form II biquad

References : Posted by robert.bielik at xponaut dot se

Notes :
The nominal implementation for biquads is the Direct Form I variant. But the Direct Form II is actually more suited for calculating the biquad since it needs only 2 memory locations, and the multiplications can be pipelined better by the compiler. In release build, I've noted a considerable speedup when compared to DF I. When processing stereo, the code below was ~ 2X faster. Until I develop a SIMD biquad that is faster, this will do.

Code :
// b0, b1, b2, a1, a2 calculated via r.b-j's cookbook
// formulae.
// m1, m2 are the memory locations
// dn is the de-denormal coeff (=1.0e-20f)

void processBiquad(const float* in, float* out, unsigned length)
for(unsigned i = 0; i < length; ++i)
register float w = in[i] - a1*m1 - a2*m2 + dn;
out[i] = b1*m1 + b2*m2 + b0*w;
m2 = m1; m1 = w;
dn = -dn;

void processBiquadStereo(const float* inL,
const float* inR,
float* outL,
float* outR,
unsigned length)
for(unsigned i = 0; i < length; ++i)
register float wL = inL[i] - a1*m1L - a2*m2L + dn;
register float wR = inR[i] - a1*m1R - a2*m2R + dn;
outL[i] = b1*m1L + b2*m2L + b0*wL;
m2L = m1L; m1L = wL;
outR[i] = b1*m1R + b2*m2R + b0*wR;
m2R = m1R; m1R = wR;
dn = -dn;


Added on : 13/01/10 by ano[ AT ]nymous[ DOT ]com
Comment :
true, this structure is faster. but it is also (even) more sensitive to coefficients changes, so it becomes unstable quite fast compaerd to the DF I form. I'd really like to know if there's a way to change coefficients and at the same time time changing the history of the filter for avoiding unstability.

Added on : 31/01/12 by earlevel
Comment :
Use direct form I (single accumulation point) when using fixed-point processors. For floating point, use direct form II transposed, which has superior numerical characteristics to direct form II (non-transposed).

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