System Identification Toolbox

Filtering Data: Focus

Depending upon the application, interest in the model can be focused on specific frequency bands. Filtering the data before the estimation, through filters that enhance these bands, improves the fit in the interesting regions. This is accomplished in the System Identification Toolbox by the property 'Focus'. For example, to enhance the fit in the frequency band between 0.02 and 0.1, (assuming a unit sampling interval) execute

• [B,A] = butter(5,[0.02 0.1])
  m = pem(Data,3,'Foc',{B,A})
  ma = arx(Data,[2 3 1],'Foc',{B,A})
  

This computes and uses a fifth order Butterworth bandpass filter with passband between the indicated frequencies. The data is filtered through this filter before fitting the transfer function from the measured inputs (G in Equation (3-53)) to the outputs. The disturbance model (H) is however estimated using the unfiltered data. Chapter 14 in Ljung (1999) discusses the role of filtering in more detail.

The command butter is from the Signal Processing Toolbox. If you do not have that toolbox, the filter can be computed using idfilt from the System Identification Toolbox.

• [Df,Mfilt] = idfilt(Data,5,[0.02 0.1])
  m = pem(Data,3,'Foc',Mfilt)
  

For a model that does not use a disturbance description (that is, H = 1 in (3-53), which corresponds to K = 0 for state-space, and na=nc=nd=0 for polynomial models), the Focus effect is the same as applying the routine to filtered data. That is,

• m = pem(Data,3,'Foc',Mfilt,'dist','none')
  m = pem(Df,3,'dist','none')
  

give the same model.

The System Identification Toolbox contains other useful commands for related problems. For example, if you want to lower the sampling rate by a factor of 5, use

• Dat5 = resample(Data,1,5);
  

Missing Data

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