# Calculating IIR DF1 coefficients

Question asked by rs85 on Dec 19, 2017
Latest reply on Jul 10, 2018 by QGingerZ

Hi there,

I'm new to DSP and was hoping for a little guidance on generating filter coefficients for an IIR Direct Form 1 filter on a BF707. I am hoping to generate filter coefficients on the fly based on user input. I have had good results so far using general C++ lowpass filter code sketches, but I would prefer to use the built in optimized functions like iirdf1_fr32, etc.

I am having trouble understanding the way that the iirdf1 function is expecting to read from the coefficient arrays-- for example, in the Audio Filter sketch included with the Blackfin dev board, the IIR uses these a and b coefficients for the lowpass filter at 1khz:

NUM_STAGES = 2;

const long double a_coeffs_low_1khz[(2 * NUM_STAGES)]     = {-3.90629342L, 5.74132017L, -3.76262386L, 0.92766971L};
const long double b_coeffs_low_1khz[(2 * NUM_STAGES) + 1] = {0.01004288L, -0.03833192L, 0.05662947L, -0.03833192L, 0.01004288L};

Many of the formulae I have found for calculating filter coefficients give an output of b0,b1,b2, and a1, a2 coefficients. Since this represents a 2-stage filter, I am unsure how to correctly populate these values (since there are 4 "a" coefficients and 5 "b" coefficients).

If anybody could point to the correct formula for calculating these coefficients or steer me in the direction of the relevant reading material it would be very much appreciated.