User`s guide

Creating Noise-Spectrum Plots

Whereas the frequency-response plot shows the response of G,the

noise-spectrum plo t shows the frequency-response of the noise mo de l H.

For input-output models, the noise spectrum is given by the following

equation:

He()ωλ

()

For time-series models (no input), the vertical axis of the noise-spectrum plot

is the same as the dynamic model spectrum. These axes are the same because

there is no input for time series and

yHe=

Note You can avoid es timating the n oise model by selecting the Output-Error

model s tructure or by setting the

DisturbanceModel property value to 'None'

for a state space model. If you choose to not estim ate a noise model for

your system, then H and the noise spectrum amplitude are equal to 1 at all

frequencies.

Displaying the Confidence Interval

In addition to the noise-s pectrum curve, you can display a conﬁdence interval

on th e plot. To learn how to show or hide conﬁdence interval, see the

description of the plot settings in “How to Plot the Noise Spectrum Using

the GUI” on page 8-42.

The conﬁdence interval corresponds to the range of power-spectrum values

with a speciﬁc probability of being the actual noise spectrum of the system.

The toolbox uses the estimated uncertainty in the model param eters to

calculate conﬁdence intervals and assumes the estimates have a Gaussian

distribution.

For example, for a 95% conﬁdenceinterval,theregionaroundthenominal

curve represents the range of values that have a 95% probability of being the

true system noise spectrum. You can specify the conﬁdence interval as a

probability (between 0 and 1) or as the number of standard deviations of a

8-41