Series Second-Order Sections

For many filter types, such as lowpass, highpass, and bandpass filters, 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^10.5 converts from ``transfer function form'', , 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 . 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

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Subsections

• Matlab Example

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.