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etfe

Estimate empirical transfer functions and periodograms

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Syntax

g = etfe(data)
g = etfe(data,M)
g = etfe(data,M,N)

Description

example

g= etfe(data)estimates a transfer function of the form:

y ( t ) = G ( q ) u ( t ) + v ( t )

datacontains time- or frequency-domain input-output data or time-series data:

  • Ifdatais time-domain input-output signals,gis the ratio of the output Fourier transform to the input Fourier transform for the data.

    For nonperiodic data, the transfer function is estimated at 128 equally-spaced frequencies[1:128]/128*pi/Ts.

    For periodic data that contains a whole number of periods (data.Period = integer), the response is computed at the frequenciesk*2*pi/periodfork = 0up to the Nyquist frequency.

  • Ifdatais frequency-domain input-output signals,gis the ratio of output to input at all frequencies, where the input is nonzero.

  • Ifdatais time-series data (no input channels),gis the periodogram, that is the normed absolute square of the Fourier transform, of the data. The corresponding spectral estimate is normalized, as described inSpectrum Normalizationand differs from thespectrumnormalization in the Signal Processing Toolbox™ product.

example

g= etfe(data,M)applies a smoothing operation on the raw spectral estimates using a Hamming Window that yields a frequency resolution of aboutpi/M. The effect ofMis similar to the effect ofMinspa.Mis ignored for periodic data. Use this syntax as an alternative tospafor narrowband spectra and systems that require large values ofM.

example

g= etfe(data,M,N)specifies the frequency spacing for nonperiodic data.

  • For nonperiodic time-domain data,Nspecifies the frequency grid[1:N]/N*pi/Tsrad/TimeUnit. When not specified,Nis 128.

  • For periodic time-domain data,Nis ignored.

  • For frequency-domain data, theNisfmin:delta_f:fmax, where[fmin fmax]is the range of frequencies indata, anddelta_fis(fmax-fmin)/(N-1)rad/TimeUnit. When not specified, the response is computed at the frequencies contained in data where input is nonzero.

Examples

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Open Live Script

Load estimation data.

loadiddata1z1;

Estimate empirical transfer function and smoothed spectral estimate.

ge = etfe(z1); gs = spa(z1);

Compare the two models on a Bode plot.

bode(ge,gs)

Figure contains 2 axes objects. Axes object 1 with title From: u1 To: y1 contains 2 objects of type line. These objects represent ge, gs. Axes object 2 contains 2 objects of type line. These objects represent ge, gs.

Open Live Script

Generate a periodic input, simulate a system with it, and compare the frequency response of the estimated model with the original system at the excited frequency points.

Generate a periodic input signal and output signal using simulation.

m = idpoly([1 -1.5 0.7],[0 1 0.5]); u = iddata([],idinput([50,1,10],'sine')); u.Period = 50; y = sim(m,u);

Estimate an empirical transfer function.

me = etfe([y u]);

Compare the empirical transfer function with the original model.

bode(me,'b*',m,'r')

Figure contains 2 axes objects. Axes object 1 with title From: u1 To: y1 contains 2 objects of type line. These objects represent me, m. Axes object 2 contains 2 objects of type line. These objects represent me, m.

Open Live Script

Perform a smoothing operation on raw spectral estimates using a Hamming Window and compare the responses.

Load data.

loadiddata1

Estimate empirical transfer functions with and without the smoothing operation.

ge1 = etfe(z1); ge2 = etfe(z1,32);

Compare the models on a Bode plot.

ge2is smoother thange1because of the effect of the smoothing operation.

bode(ge1,ge2)

Figure contains 2 axes objects. Axes object 1 with title From: u1 To: y1 contains 2 objects of type line. These objects represent ge1, ge2. Axes object 2 contains 2 objects of type line. These objects represent ge1, ge2.

Open Live Script

估计经验——一个较低的传输函数d high-frequency spacings and compare the responses.

Load data.

loadiddata9

Estimate empirical transfer functions with low and high frequency spacings.

ge1 = etfe(z9,[],32); ge2 = etfe(z9,[],512);

Plot the output power spectrum of the two models.

spectrum(ge1,'b.-',ge2,'g')

Figure contains an axes object. The axes object with title From: e@y1 To: y1 contains 2 objects of type line. These objects represent ge1, ge2.

Input Arguments

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Estimation data, specified as aniddataobject. The data can be time- or frequency-domain input/output signals or time-series data.

Frequency resolution, specified as a positive scalar.

Frequency spacing, specified as a positive scalar. For frequency-domain data, the default frequency spacing is the spacing inherent in the estimation data.

Output Arguments

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Transfer function estimate, returned as anidfrdmodel.

Information about the estimation results and options used is stored in the model'sReportproperty.Reporthas the following fields:

Report Field Description
Status

Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.
Method

Estimation command used.
WindowSize

Size of the Hamming window.
DataUsed

Attributes of the data used for estimation, returned as a structure with the following fields.

Field Description
Name

Name of the data set.
Type

Data type.
Length

Number of data samples.
Ts

Sample time.
InterSample

Input intersample behavior, returned as one of the following values:

  • 'zoh'— Zero-order hold maintains a piecewise-constant input signal between samples.

  • 'foh'— First-order hold maintains a piecewise-linear input signal between samples.

  • 'bl'— Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.
InputOffset

Offset removed from time-domain input data during estimation. For nonlinear models, it is[].
OutputOffset

Offset removed from time-domain output data during estimation. For nonlinear models, it is[].

For more information on usingReport, seeEstimation Report.

Version History

Introduced before R2006a

See Also

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