System Identification Toolbox™

idfilt

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

Syntax

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

Description

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 idmodel 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 in rad/s. 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 example, to define a stopband between ws1 and ws2, use

  filter = [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.

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.

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 property 'Focus' (see Algorithm Properties) than just to prefilter the data. The proper values for 'Focus' are the same as the argument filter in idfilt.

Algorithm

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.

References

Ljung (1999), Chapter 14.

See Also

ident

idfrd