# Documentation

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## Estimation Input Signals

Frequency response estimation uses either sinestream or chirp input signals.

Sinusoidal SignalWhen to Use
SinestreamRecommended for most situations. Especially useful when:
• Your system contains strong nonlinearities.

• You require highly accurate frequency response models.

ChirpUseful when:
• Your system is nearly linear in the simulation range.

• You want to quickly obtain a response for a lot of frequency points.

### What Is a Sinestream Signal?

A sinestream signal consists of several adjacent sine waves of varying frequencies. Each frequency excites the system for a period of time.

#### How Frequency Response Estimation Treats Sinestream Inputs

Frequency response estimation using `frestimate` performs the following operations on a sinestream input signal:

1. Injects the sinestream input signal you design, uest(t), at the linearization input point.

2. Simulates the output at the linearization output point.

`frestimate` adds the signal you design to existing Simulink® signals at the linearization input point.

3. Discards the `SettlingPeriods` portion of the output (and the corresponding input) at each frequency.

The simulated output at each frequency has a transient portion and steady state portion. `SettlingPeriods` corresponds to the transient components of the output and input signals. The periods following `SettlingPeriods` are considered to be at steady state.

4. Filters the remaining portion of the output and the corresponding input signals at each input frequency using a bandpass filter.

When a model is not at steady state, the response contains low-frequency transient behavior. Filtering typically improves the accuracy of your model by removing the effects of frequencies other than the input frequencies. These frequencies are problematic when your sampled data has finite length. These effects are called spectral leakage.

`frestimate` uses a finite impulse response (FIR) filter. The software sets the filter order to match the number of samples in a period such that any transients associated with filtering appear only in the first period of the filtered steady-state output. After filtering, `frestimate` discards the first period of the input and output signals.

You can specify to disable filtering during estimation using the signal `ApplyFilteringInFRESTIMATE` property.

5. Estimates the frequency response of the processed signal by computing the ratio of the fast Fourier transform of the filtered steady-state portion of the output signal yest(t) and the fast Fourier transform of the filtered input signal uest(t):

To compute the response at each frequency, `frestimate` uses only the simulation output at that frequency.

### What Is a Chirp Signal?

The swept-frequency cosine (chirp) input signal excites your system at a range of frequencies, such that the input frequency changes instantaneously.

Alternatively, you can use the sinestream signal, which excites the system at each frequency for several periods.