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.

Filter data using user-defined passbands, general filters, or Butterworth filters

`Zf = idfilt(Z,filter)`

Zf = idfilt(Z,filter,causality)

Zf = idfilt(Z,filter,'FilterOrder',NF)

`Zf = idfilt(Z,filter)`

filters data using
user-defined passbands, general filters, or Butterworth filters. `Z`

is
the data, defined as an `iddata`

object. `Zf`

contains
the filtered data as an `iddata`

object. The filter
can be defined in three ways:

As an explicit system that defines the filter.

filter = idm or filter = {num,den} or filter = {A,B,C,D}

`idm`

can be any SISO identified linear model or LTI model object. Alternatively the filter can be defined as a cell array`{A,B,C,D}`

of SISO state-space matrices or as a cell array`{num,den}`

of numerator/denominator filter coefficients.As a vector or matrix that defines one or several passbands.

filter=[[wp1l,wp1h];[ wp2l,wp2h]; ....;[wpnl,wpnh]]

The matrix is

`n`

-by-2, where each row defines a passband. A filter is constructed that gives the union of these passbands. For time-domain data, it is computed as cascaded Butterworth filters or order NF. The default value of NF is`5`

.For time-domain data — The passbands are in units of

`rad/TimeUnit`

, where`TimeUnit`

is the time units of the estimation data.For frequency-domain data — The passbands are in the frequency units (

`FrequencyUnit`

property) of the estimation data.

For example, to define a stopband between

`ws1`

and`ws2`

, usefilter = [0 ws1; ws2,Nyqf]

where

`Nyqf`

is the Nyquist frequency.For frequency-domain data, only the frequency response of the filter can be specified.

filter = Wf

Here

`Wf`

is a vector of possibly complex values that define the filter's frequency response, so that the inputs and outputs at frequency`Z.Frequency(kf)`

are multiplied by`Wf(kf)`

.`Wf`

is a column vector of length = number of frequencies in`Z`

. If the data object has several experiments,`Wf`

is a cell array of length = # of experiments in`Z`

.

`Zf = idfilt(Z,filter,causality)`

specifies
causality. For time-domain data, the filtering is carried out in the
time domain as causal filtering as default. This corresponds to a
last argument `causality = 'causal'`

. With ```
causality
= 'noncausal'
```

, a noncausal, zero-phase filter is used for
the filtering (corresponding to `filtfilt`

in the Signal
Processing Toolbox™ product).

For frequency-domain data, the signals are multiplied by the
frequency response of the filter. With the filters defined as passband,
this gives ideal, zero-phase filtering (“brickwall filters”).
Frequencies that have been assigned zero weight by the filter (outside
the passband, or via the frequency response) are removed from the `iddata`

object `Zf`

.

`Zf = idfilt(Z,filter,'FilterOrder',NF)`

specifies
the filter order. The time domain filters in the pass-band case are
calculated as cascaded Butterworth pass-band and stop-band filters.
The orders of these filters are 5 by default, which can be changed
to an arbitrary integer `NF`

.

It is common practice in identification to select a frequency
band where the fit between model and data is concentrated. Often this
corresponds to bandpass filtering with a passband over the interesting
breakpoints in a Bode diagram. For identification where a disturbance
model is also estimated, it is better to achieve the desired estimation
result by using the `'WeightingFilter'`

option of
the estimation command than just to prefilter the data. The values
for `'WeightingFilter'`

are the same as the argument `filter`

in `idfilt`

.

The Butterworth filter is the same as `butter`

in
the Signal
Processing Toolbox product. Also, the zero-phase filter
is equivalent to `filtfilt`

in that toolbox.

Ljung (1999), Chapter 14.

Was this topic helpful?