IIR Cascaded Second-Order Sections Form Structures (Digital Filter Design Toolkit)

The transfer function of an infinite impulse response (IIR) filter with a Cascaded Second-Order Sections Form structure is defined as follows:

where z is a complex variable, N is the number of sections, a is the set of reverse coefficients, and b is the set of forward coefficients.

IIR Cascaded Second-Order Sections Form I

Comparing with the IIR Direct Form structures, the IIR Cascaded Second-Order Sections Form structures have more computational complexity. However, the cascaded structures help alleviate finite word length effects. The following figure represents the IIR Cascaded Second-Order Sections Form I structure. Refer to the Understanding Filter Structure Graphs topic for information that helps you read and understand a filter structure graph.

IIR Cascaded Second-Order Sections Form II

The following figure represents the IIR Cascaded Second-Order Sections Form II structure. Comparing with Form I, this structure uses the same number of mathematical operations but fewer delays.

IIR Cascaded Second-Order Sections Form I Transposed

The following figure represents the IIR Cascaded Second-Order Sections Form I Transposed structure.

IIR Cascaded Second-Order Sections Form II Transposed

The following figure represents the IIR Cascaded Second-Order Sections Form II Transposed structure.

The IIR Cascaded Second-Order Sections Form I and Form II Transposed structures implement forward coefficients first. The Form I Transposed and Form II structures implement reverse coefficients first. The IIR Cascaded Second-Order Sections Form II structure has the same computational complexity as the Form I, but the Form I requires more memory for saving internal states. The Form II Transposed is the structure that you most frequently use. Using the Form I and Form II and their transposed structures has the same advantages and disadvantages as using the FIR Direct Form and FIR Direct Form Transposed structures.