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freqresp - Frequency response data from linear models

Alternative

idfrd computes the same information as freqresp and stores it in the idfrd model object.

Syntax

H = freqresp(m) [H,w,covH] = freqresp(m,w)

Description

H = freqresp(m) returns the frequency response H of the model m at default frequencies determined from the dynamics of the model. For idmodel models, computes the frequency response of the model. For idfrd models, extracts the frequency data from the model object. If m contains nonzero delays (stored as m.InputDelay), these delays are absorbed into the returned frequency response.

[H,w,covH] = freqresp(m,w) returns the frequency response H of the model m

at frequencies w. For idfrd models with input channels, the frequency response is H = m.ResponseData and the covariance of the response is covH = m.CovarianceData. For time-series idfrd models (power spectra), the frequency response is H = m.SpectrumData and the covariance of the response is covH = m.NoiseCovariance.

Tip For a SISO model, use H(:) to obtain a vector of the frequency response. If models containing input channels, you can get the spectrum information of the noise (output disturbance) signal using freqresp(m('n')).

Inputs

m

Name of the idmodel or idfrd model object.

w

Frequencies for computing the frequency response, specified as a vector of real values in rad/s.

Note If you do not specify w, freqresp returns the frequency response at default frequencies determined from the dynamics of the model.

Outputs

H

Frequency response data of the model.

If m has ny outputs and nu inputs, and w contains Nw frequencies, the output H is an ny-by-nu-by-Nw array such that H(:,:,k) is a complex-valued response at frequency w(k).

w

Frequencies of the response, returned as a vector of real values in rad/s.

covH

For a model with input channels, covariance of the response of a model that is a 5-D array. covH(ky,ku,k,:,:) is the 2-by-2 covariance matrix of the response from the input ku to the output ky at frequency w(k). The (1,1) element is the variance of the real part, the (2,2) element is the variance of the imaginary part, and the (1,2) and (2,1) elements are the covariance between the real and imaginary parts.

Tip squeeze(covH(ky,ku,k,:,:)) returns the covariance matrix of the corresponding response.

For a time-series model (no input channels), H is an ny-by-ny-by-Nw array of the power spectrum of the outputs. Thus, H(:,:,k) is the spectrum matrix at frequency w(k). The element H(k1,k2,k) is the cross spectrum between outputs k1 and k2 at frequency w(k). When k1 = k2, this is the real-valued power spectrum of output k1.

covH is then the covariance of the estimated spectrum H such that covH(k1,k1,k) is the variance of the power spectrum estimate of output k1 at frequency w(k). No information about the variance of the cross spectra is given; that is, covH(k1,k2,k) = 0 for k1 not equal to k2.

`bode`
`etfe`
`ffplot`
`idfrd`
`nyquist`
`spa`
`spafdr`