User`s guide

3 Linear Model Identification
Identifying Frequency-Response Models
In this section...
“What Is a Frequency-Response M odel?” on page 3-2
“Data Supported by Frequency-Response Models” on p age 3-3
“How to Estimate F requency-Response Models in the GUI” on page 3-3
“How to Estimate Frequency-Response Models at the Comm and Line” on
page 3-5
“Options for Computing Spectral Models” on page 3 -5
“Options for Frequency Resolution” on page 3-6
“Spectral Analysis Algorithm” on page 3-8
“Understanding Spectrum Norm alization” on page 3-11
What Is a Frequency-Response Model?
You can estimate frequency-response models and visualize the responses on
a B ode plot, which shows the am plitude change and the phase shift as a
function o f the sinusoid frequency.
For a discrete-time system sampled with a time interval T,the
frequency-response model G(z) relates the Z-transforms of the input U(z)
and output Y(z):
Yz GzUz() () ()=
The frequency-response function describes the steady-state response of a
system to sinusoidal inputs. For a linear system, a sinusoidal input of a
specific frequency results in an output that is also a sinusoid with the same
frequency, but with a different amplitude and phase. The frequency response
describes the amplitude change and phase shift as a function of frequency.
In other words, the frequency-response function, G(e
iwT
),istheLaplace
transformoftheimpulseresponsethatisevaluatedontheimaginaryaxis.
The frequency-response function is the transfer function G(z) evaluated on
the unit circle.
3-2