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Modal Representation
When the state transition matrix
is diagonal, we have the
so-called modal representation. In the single-input,
single-output (SISO) case, the general diagonal system looks like
Since the state transition matrix is diagonal, the modes are decoupled,
and we can write each mode's time-update independently:
Thus, the diagonalized state-space system consists of
parallel one-pole systems. See §9.2.2
and §6.8.7 regarding the conversion of direct-form filter
transfer functions to parallel (complex) one-pole form.
Subsections
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