Biquad IIR Filter Design Tool in Octave

The Infinite Impulse Response (IIR) biquad filter is a simple to implement digital filter while allowing the modification of any signal in a variety of strategic ways. These filters can be then cascaded allowing further control of the resulting output.

biquadratic z-domain transfer function

It should be noted that the coefficients a and b are swapped compared to those shown on wikipedia and biquad filter coefficients cookbook. This convention was used by used by EAR level engineering. Using this equation the biquad filter can be easily implemented using direct form I or direct form II.

Direct Form I Equation:

Direct Form I

Direct Form II Equations:

Direct Form II Equations

Once the filter has been implemented the coefficients can be calculated using the filter design tool.

Example high pass filter design with filter design tool
Parameters used to calculate various filter types