Behavior of the Fit Outside the Fit Region
The max order algorithm finds only those poles and zeros needed to provide a
good match to the measurement over the fit region. Thus, the frequency
response of the curve-fit model outside the fit region tends to follow the
behavior of the response near the boundaries of the fit region. The curve fitter
inserts simple poles or complex-conjugate pole pairs (or zeros) outside the fit
region as needed to obtain a good fit to the response inside the fit region. Poles
and zeros found outside the fit region usually result in a gradual drop-off in the
response. You can use the [
FIT TO SYNTH
] softkey to synthesize the
frequency response over the entire measurement span to evaluate the model
accuracy outside of the fit region.
Understanding the Effects of Poles and Zeros Outside the Fit Region
With the following example, you can see the effect that poles and zeros outside
the fit region have on the response inside the fit region. We will take the poles
and zeros shown in figure 16-1, synthesize them over a span of 25.6 kHz, and
fit the data over a smaller region (1.28 kHz to 3.2 kHz).
The poles and zeros shown in figure 16-1 are the same poles and zeros used in
chapter 16 (“Synthesis”), with an additional zero at 65 kHz and a pole at
45 kHz. The additional pole and zero are both outside the fit region but have a
small effect on the response inside the fit region. This small effect is not
sufficient for the curve fitter to identify the pole at 45 kHz and the zero at
65 kHz—however, the effect is sufficient for the curve fitter to compensate
withanewzero,toreplacethepoleat45kHzandzeroat65kHz. Thecurve
fit result is shown in figure 16-2. Although the pole-zero models look quite
different, figure 16-3 shows the frequency responses to be nearly the same over
the fit region.
Agilent 35607A
Curve Fit Option 1D3 Operator's Guide
16-18
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