Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution

`g = spafdr(data)`

g = spafdr(data,Resol,w)

`g = spafdr(data)`

estimates the transfer
function and noise spectrum *Φ _{υ}* of
the general linear model

$$y(t)=G(q)u(t)+v(t)$$

where *Φ _{υ}*(

`data`

contains
the output-input data as an `iddata`

object. The
data can be complex valued, and either time or frequency domain. It
can also be an `idfrd`

object containing frequency-response
data. `g`

is an `idfrd`

object
with the estimate of $$G\left({e}^{i\omega}\right)$$ at the frequencies `w`

. `g`

also includes
information about the spectrum estimate of `g`

. The normalization of
the spectrum is the same as described in `spa`

.Information about the estimation results and options used is
stored in the model's `Report`

property. `Report`

has
the following fields:

`Status`

— Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.`Method`

— Estimation command used.`WindowSize`

— Frequency resolution.`DataUsed`

— Attributes of the data used for estimation. Structure with the following fields:`Name`

— Name of the data set.`Type`

— Data type.`Length`

— Number of data samples.`Ts`

— Sample time.`InterSample`

— Input intersample behavior.`InputOffset`

— Offset removed from time-domain input data during estimation.`OutputOffset`

— Offset removed from time-domain output data during estimation.

`g = spafdr(data,Resol,w)`

specifies frequencies
and frequency resolution.

The frequency variable `w`

is either specified
as a row vector of frequencies, or as a cell array `{wmin,wmax}`

.
In the latter case the covered frequencies will be 50 logarithmically
spaced points from `wmin`

to `wmax`

.
You can change the number of points to `NP`

by entering `{wmin,wmax,NP}`

.

Omitting `w`

or entering it as an empty matrix
gives the default value, which is 100 logarithmically spaced frequencies
between the smallest and largest frequency in data. For time-domain
data, this means from `1/N*Ts`

to `pi*Ts`

,
where `Ts`

is the sample time of data and `N`

is
the number of data.

The argument `Resol`

defines the frequency
resolution of the estimates. The resolution (measured in rad/s) is
the size of the smallest detail in the frequency function and the
spectrum that is resolved by the estimate. The resolution is a tradeoff
between obtaining estimates with fine, reliable details, and suffering
from spurious, random effects: The finer the resolution, the higher
the variance in the estimate. `Resol`

can be entered
as a scalar (measured in rad/s), which defines the resolution over
the whole frequency interval. It can also be entered as a row vector
of the same length as `w`

. Then `Resol(k)`

is
the local, frequency-dependent resolution around frequency `w(k)`

.

The default value of `Resol`

, obtained by omitting
it or entering it as the empty matrix, is `Resol(k) = 2(w(k+1)-w(k))`

,
adjusted upwards, so that a reasonable estimate is guaranteed. In
all cases, the resolution is returned in the variable `g.Report.WindowSize`

.

Was this topic helpful?