How Auto Order Defmes A Good Fit; Effect On Weighting Function - HP 3563A Operating Manual

Curve Fit
How Coherence is Used in Curve Fitting
How Auto Order Defines a Good Fit
To prevent the auto-order algorithm from always searching to the upper bounds, a variance function
is used to establish an error tolerance that gives the auto-order algorithm some margin when fitting
contaminated data.
The auto-order algorithm uses the number of averages and the coherence function to calculate a
variance function on the measurement. The auto-order algorithm calculates an error-to-signal level,
and compares this to a noise-to-signal level. When the error-to-signal level drops below the
noise-to-signal level, the fit is defined as good.
function corresponds to
20
noise level at dB below the signal level, and
the signal level. Since the variance function is used, rather than the coherence function, these
figures are merely presented as typical - additional averaging lowers the measurement noise level
in the noise-to-signal level calculation.
The curve-fit routine calculates a psuedo coherence when fitting to swept sine measurements.
Measurement coherence in swept sine is much higher than obtained with FFT-based measurements.
A psuedo coherence allows for a more realistic error tolerance in the presence of nonlinearities.

Effect on Weighting Function

The auto-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
Also,
regions of low variance are not n
emphasizes regions about peaks, valleys (under some conditions), and frequencies near dc if the
variance is low.
1 6-36
As
10
dB in the noise-to-signal level. For example,
-
0.9999
ecess
a rily emphasized: the weighting function only
a rough approximation, each
corresponds to a noise level at
.9
in the coherence
0.99
corresponds to a
40
dB below
AUTO WEIGHT
is used.