Series Second-Order Sections

For many filter types, such as lowpass, highpass, and bandpass filters, and for filters which need to vary over time, a good choice of implementation structure is often series second-order sections. In fixed-point applications, the ordering of the sections can be important.

The matlab function tf2sos^10.3 converts from ``transfer function form'', $H(z)=B(z)/A(z)$, to series ``second-order-section'' form. For example, the line

  BAMatrix = tf2sos(B,A);

converts the real filter specified by polynomial vectors B and A to a series of second-order sections (biquads) specified by the rows of BAMatrix. Each row of BAMatrix is of the form $[b_0,b_1,b_2,\,1,a_1,a_2]$. The function tf2sos may be implemented simply as a call to tf2zp followed by a call to zp2sos, where the zp form of a digital filter consists of its (possibly complex) zeros, poles, and an overall gain factor:

function [sos,g] = tf2sos(B,A)
[z,p,g]=tf2zp(B(:)',A(:)'); % Direct form to (zeros,poles,gain)
sos=zp2sos(z,p,g); % (z,p,g) to series second-order sections