The Weighting Function
Like coherence, the weighting function is a real-valued function of frequency
which varies between 0.0 and 1.0. The weighting function is used to
emphasize important areas of the curve region during a curve fit and to
de-emphasize areas of high variance. The weighting function can be
automatically calculated from measured data, or you can create your own
weighting function manually.
When you use auto weight, the curve-fitter automatically derives a weighting
function based on an initial estimate of pole-zero locations and on the variance
function. The auto-weighting algorithm tends to emphasize low frequencies
and peaks. Thus, as the frequency increases, the emphasis is on resonances
(complex poles) rather than simple poles that may change only the rate of
amplitude roll-off. This weighting function is placed in the selected weight
register during the curve fit.
When you use user weight, the curve fitter uses the weighting function stored
in the selected weight register. A typical application of user weight is to
modify a weighting function created in a previous curve fit using auto weight.
When a curve fit using auto weight is finished, you can use data edit to modify
the contents of the data register selected as the weight register. Then select
user weight and re-run the curve fit. The curve fitter does not modify the
weight register when user weight is selected.
For synthesized data, the weighting function is not critical to obtaining a good
fit, so the auto-weighting algorithm creates a weighting function which has a
value of 1.0 at all frequencies.
Under most circumstances the auto-weighting algorithm creates an acceptable
weighting function. When the curve fit result doesn’t match the measured
frequency response in an area that you consider important, it is probably
because the auto-weighting algorithm has de-emphasized that portion of the
response. In this situation, the best approach to obtaining an acceptable fit is to
edit the existing weighting function and try higher weighting values.
How Coherence Affects the Weighting Function
The max order algorithm uses the number of averages and the coherence
function to calculate a variance function on the measurement. Regions of high
variance (low coherence, depending upon the number of averages) are not
emphasized in the weighting function when you use auto weighting. Also,
regions of low variance are not necessarily emphasized: the weighting function
only emphasizes regions around peaks and frequencies near dc if the variance
is low.
Agilent 35607A
Operator's Guide Curve Fit Option 1D3
16-23
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