Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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Curve Fitting and Synthesis 2-75
SR785 Dynamic Signal Analyzer
Curve Fitting and Synthesis
Often, the frequency response measurements made in the FFT and Swept Sine
measurement groups need to be compared to a theoretical model of the device's behavior.
This comparison is the job of Curve Fitting and Synthesis. In curve fitting, the analyzer
extracts the best fit parameters of a linear frequency response function from a measured
frequency response function. In Curve Synthesis, the analyzer transforms a set of
frequency response parameters into an SR785 frequency response measurement which
can be compared with the measured data.
Curve Tables
Both curve fitting and curve synthesis use the SR785's two Curve Tables. The curve
tables allow entry and editing of frequency response parameters in one of three formats:
polynomial, pole-zero, and pole residue. Once parameters have been entered into the
curve tables the corresponding frequency response function can be synthesized into a
trace for comparison with measured data.
Polynomial
In this format, the curve table represents a frequency response function as the ratio of
two polynomials in the complex frequency variable s.
Freq sp s Gain
b s b s b
a s a s a
n
n
n
n
m
m
m
m
. Re .( )
( ... )
...
= ∗
+ + +
+ + +
−
−
−
−
1
1
0
1
1
0
The curve tables allow entry of both the numerator and denominator coefficients as well
as the order of the numerator and denominator polynomials. The curve table also
contains a constant gain factor which multiplies the polynomials.
Pole-Zero
In the pole-zero format, the numerator and denominator polynomials are factored so that
the frequency response curve is described by the ratio of the products of the poles and
zeros: To ensure a real impulse response, all complex poles and zeros only occur in
complex conjugate pairs.
Freq sp s Gain
s z s z s z
s p s p s p
n n
m m
. Re .( )
( )( )...( )
( )( )...( )
= ∗
− − −
− − −
−
−
1 0
1 0
Pole Residue
In the pole residue format a partial fraction expansion of the pole-zero form is performed
to yield the frequency response as a sum of single pole terms weighted by residues.
Freq sp s Gain
R
s p
R
s p
R
s p
m
m
m
m
. Re .( )
( ) ( )
...
( )
= ∗
−
+
−
+ +
−






−
−
1
1
0
0
Once again, the residues corresponding to complex conjugate pole pairs are complex
conjugates themselves.