Chapter 2 additive error reduction, Introduction, Introduction -1 – National Instruments NI MATRIXx Xmath User Manual
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Additive Error Reduction
This chapter describes additive error reduction including discussions of
truncation of, reduction by, and perturbation of balanced realizations.
Introduction
Additive error reduction focuses on errors of the form,
where G is the originally given transfer function, or model, and G
r
is the
reduced one. Of course, in discrete-time, one works instead with:
As is argued in later chapters, if one is reducing a plant that will sit inside
a closed loop, or if one is reducing a controller, that again is sitting in a
closed loop, focus on additive error model reduction may not be
appropriate. It is, however, extremely appropriate in considering reducing
the transfer function of a filter. One pertinent application comes specifically
from digital filtering: a great many design algorithms lead to a finite
impulse response (FIR) filter which can have a very large number of
coefficients when poles are close to the unit circle. Model reduction
provides a means to replace an FIR design by a much lower order infinite
impulse response (IIR) design, with close matching of the transfer function
at all frequencies.
G j
ω
( ) G
r
j
ω
( )
–
∞
G e
j
ω
(
) G
r
e
j
ω
(
)
–
∞