Single-Input, Single-Output (SISO) FDN
Note that when , this system is capable of realizing any transfer function of the form
The more general case shown in Fig.2.29 can be handled in one of two ways: (1) the matrices can be augmented to order such that the three delay lines are replaced by unit-sample delays, or (2) ordinary state-space analysis may be generalized to non-unit delays, yielding
In FDN reverberation applications, , where is an orthogonal matrix, for reasons addressed below, and is a diagonal matrix of lowpass filters, each having gain bounded by 1. In certain applications, the subset of orthogonal matrices known as circulant matrices have advantages .
FDN and State Space Descriptions