### FDN and State Space Descriptions

When
in Eq.(2.10), the FDN (Fig.2.28)
reduces to a normal *state-space model* (§1.3.7),

The matrix is the

*state transition matrix*. The vector holds the

*state variables*that determine the state of the system at time . The

*order*of a state-space system is equal to the number of state variables,

*i.e.*, the dimensionality of . The input and output signals have been trivially redefined as

to follow normal convention for state-space form.

Thus, an FDN can be viewed as a generalized state-space model for a class of th-order linear systems--``generalized'' in the sense that unit delays are replaced by arbitrary delays. This correspondence is valuable for analysis because tools for state-space analysis are well known and included in many software libraries such as with matlab.

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Time Varying Comb Filters