Fitting Measurements With Delay - HP 3563A Operating Manual

Curve Fit
Fitting Measurements With Del a y

Fitting Measurements With Delay

Both the s- and z-domain curve fitters can have trouble finding a model when pure delay is present
in the measurement.
S-Domain
Any pure delay in a system affects the phase of the frequency response without affecting its
magnitude. If these delays are known, they should be entered into the s-domain curve fit table
before starting a curve fit. Pure delays cannot be modeled with a finite-order rational polynomial
in the s domain. For more information on the effects of excess phase refer to product note
HP "Curve Fitting in the HP
3562A-3,
Z-Domain
In the z-domain there are two types of delay - partial and full sample delays.
curve fitter, it is best to remove the effects of the delays on the frequency response by entering the
delay value into the curve fit table before starting a curve fit. Partial sample delays must be entered
as a delay in the curve-fit table.
delay, or as a fi x ed pole at the origin.
Full sample delays can be modeled in the z domain as z
delays. However, noise causes these poles to appear scattered near the origin. Thus, best results are
obtained by f IXing n poles at the origin.
Example: Curve Fitting to FIR filters
Any z-domain model which contains more zeros than poles is non-causal (since z-domain curve-fit
models are only expressed in +Zpower) unless delay terms are added. You should add poles at the
origin to make such a design causal. However, the phase then has a linear ramp. Thus, you may
want to resynthesize the transfer function.
The product note on z-domain curve fitting mentions
more zeros than poles. Note that
expressed in negative powers of z. Expressing an
a pole at the origin with a multiplicity equal to the system order. Thus, in positive powers of z, an
FIR
filter has an equal number of poles and zeros and does not require extra delay terms to make it
causal. Alternatively, the filter can be expressed as the product of z
multiple-order pole at the origin), where k is the system order, and an all-zero filter expressed in
z.
positive powers of
Poles at the origin correspond to unit sample delays (since poles at the origin appear as z
This delay needs to be taken out of the curve-fit process before curve fitting to an
poles at the origin in the curve-fit table (that is, place
account for delay before curve fitting, poles appear in a scatter pattern near the origin. Larger
quantization errors move these farther from the origin.
1 6-38
3562A".
full sample delay can be entered into the curve-fit table as either a
A
-
FIR
filters can be thought of as all-zero transfer functions if
FIR
FIR
filter in terms of positive powers of z produces
0.0
As
n, where n refers to the number of sample
filters as an example of a design with
k
(a consequence of the
-
entries in the poles column). If you do not
with the s-domain
k
terms).
-
filter by f IXing
FIR