Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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2-76 Curve Fitting and Synthesis
SR785 Dynamic Signal Analyzer
If the order of the numerator in the polynomial representation is equal to or greater than
the order of the denominator polynomial, the Pole-Residue representation will contain an
additional polynomial whose order is the difference between the numerator order and
denominator order. This polynomial is added to the equation shown above. The
coefficients of this extra polynomial cannot be adjusted by the user; use one of the other
representations if this is necessary.
The SR785 will convert curve parameters between any of these three formats. Results of
curve fits are always initially presented in pole-zero format although they can always be
subsequently converted to any format.
Frequency Scale
Often a theoretical model frequency response function will be specified with respect to a
nominal frequency, such as 1 Hz. The curve table contains a frequency scale parameter
to allow such a nominal transfer function to be synthesized to any actual frequency. In
terms of the pole zero representation, the poles and zeros are all multiplied by the scaling
factor before synthesizing the curve. When fitting, after the poles and zeros
corresponding to the measured frequency response function are determined, the values
are all divided by the Frequency Scale factor. For example, if the curve table contains a
pole (s-1), and the frequency scale is 1000, this will create a pole at 1 kHz when
synthesizing the table.
Delay
The three formats for a frequency response function discussed above cannot model a
pure delay term of the form exp(-sT), where T is the delay time. Because of this, and
because measured frequency response data often includes delay, a delay parameter is
included in the curve table. On synthesis the analyzer multiplies the Frequency Response
function by the delay factor exp(-sT). When fitting, the input data is divided by exp(-sT)
before the curve parameters are calculated. Note that the curve fitter will not fit an
appropriate value of the delay- this value must be supplied by the user.
Trace
The curve table also contains a field which determines which trace will be written to
when the curve is synthesized.
Curve Fitting
Before fitting a measured frequency response function several setup parameters must be
specified. The fit region determines the region of the active display that will be fit. The
number of poles and zeros determine the order of the frequency response function which
will be fit to the measured data. The active display must be in the FFT or Swept Sine
measurement group to be fit.
When the user presses Start Fit, the analyzer computes in a single pass, the best fit
parameters for the active display using the Delay and Frequency Scale parameters for
Curve Table 1. These parameters are then placed in curve table 1 in the pole-zero
representation. Finally, Curve Table 1 is synthesized and the synthesized trace is placed
in the non-active display so it can be compared to the original data in the active display.