This time response has not reached steady state.

This plot shows a steady-state time response.

Because frequency response estimation requires steady-state input and output signals, transients produce inaccurate estimation results.

For sinestream input signals, transients sometimes interfere with the estimation either directly or indirectly through spectral leakage. For chirp input signals, transients interfere with estimation.

After you try the suggested actions, recompute the estimation either:

• At all frequencies, as described in Estimating Frequency Response

• In a particular frequency range (only for sinestream input signals)

To recompute the estimation in a particular frequency range:

1. Determine the frequencies for which you want to recompute the estimation results. Then, extract a portion of the sinestream input signal at these frequencies using fselect.

   For example, these commands extract a sinestream input signal between 10 and 20 rad/s from the input signal input:

   input2 = fselect(input,10,20);

2. Modify the properties of the extracted sinestream input signal input2, as described in Modifying Input Signals for Estimation.

3. Estimate the frequency response sysest2 with the modified input signal using frestimate.

4. Merge the original estimated frequency response sysest and the recomputed estimated frequency response sysest2:

   1. Remove data from sysest at the frequencies in sysest2 using fdel. For example:

      sysest = fdel(sysest,input2.Frequency)

   2. Concatenate the original and recomputed responses using fcat. For example:

      sys_combined = fcat(sysest2,sysest)

You can analyze the recomputed frequency response, as described in Analyzing Estimated Frequency Response.

For an example of frequency response estimation with time-varying source blocks, see Effects of Time-Varying Source Blocks on Frequency Response Estimation

When the FFT plot shows large amplitudes at frequencies other than the input signal, your model is operating outside the linear range. This condition can causes problems when you want to analyze your linear system response to small perturbations.

For models operating in the linear range, the input amplitude A₁ in y(t) must be larger than the amplitudes of other harmonics, A₂ and A₃.

Adjust the amplitude of your input signal to decrease the impact of other harmonics, and repeat the estimation, as described in Estimating Frequency Response. Typically, you should decrease the input amplitude level to keep the model operating in the linear range.

For more information about modifying signal amplitudes, see one of the following:

• frest.Sinestream

• frest.Chirp

• Modifying Input Signals for Estimation

When the time response grows without bound, frequency response estimation results are inaccurate. Frequency response estimation is only accurate close to the operating point.

Try the suggested actions listed the table and repeat the estimation, as described in Estimating Frequency Response.

Discontinuities or noise in the time response indicate that the amplitude of your input signal is too small to overcome the effects of the discontinuous blocks in your model. Examples of discontinuous blocks include Quantizer, Backlash, and Dead Zones.

If you used a sinestream input signal and estimated with filtering, turn filtering off in the Simulation Results Viewer to see the unfiltered time response.

The following model with a Quantizer block shows an example of the impact of an input signal that is too small. When you estimate this model, the unfiltered simulation output includes discontinuities.

Increase the amplitude of your input signal, and repeat the estimation, as described in Estimating Frequency Response.

With a larger amplitude, the unfiltered simulated output of the model with a Quantizer block is smooth.

For more information about modifying signal amplitudes, see one of the following:

• frest.Sinestream

• frest.Chirp

• Modifying Input Signals for Estimation

When the time response is noisy, frequency response estimation results may be biased.

frestimate does not support estimating frequency response estimation of Simulink models with blocks that model noise. Locate such blocks with frest.findSources and disable them using the BlocksToHoldConstant option of frestimate.

If you need to estimate a model with noise, use frestimate to simulate an output signal from your Simulink model for estimation—without modifying your model. Then, use the Signal Processing Toolbox™ or System Identification Toolbox software to estimate a model.

To simulate the output of your model in response to a specified input signal:

1. Create a random input signal. For example:

   in = frest.Random('Ts',0.001,'NumSamples',1e4);
   

   You can also specify your own custom signal as a timeseries object. For example:

   t = 0:0.001:10;
   y = sin(2*pi*t);
   in_ts = timeseries(y,t);

2. Simulate the model to obtain the output signal. For example:

   [sysest,simout] = frestimate(model,op,io,in_ts)
   

   The second output argument of frestimate, simout, is a Simulink.Timeseries object that stores the simulated output. in_ts is the corresponding input data.

3. Generate timeseries objects before using with other MathWorks^® products:

   input = generateTimeseries(in_ts);
   output = simout{1}.Data;

   You can use data from timeseries objects directly in Signal Processing Toolbox software, or convert these objects to System Identification Toolbox data format. For examples, see Estimating Frequency Response Models with Noise Using Signal Processing Toolbox and Estimating Frequency Response Models with Noise Using System Identification Toolbox.

For a related example, see Effects of Noise on Frequency Response Estimation.