This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

What is a Frequency-Response Model?

A frequency-response model is the frequency response of a linear system evaluated over a range of frequency values. The model is represented by an idfrd model object that stores the frequency response, sample time, and input-output channel information.

The frequency-response function describes the steady-state response of a system to sinusoidal inputs. For a linear system, a sinusoidal input of a specific frequency results in an output that is also a sinusoid with the same frequency, but with a different amplitude and phase. The frequency-response function describes the amplitude change and phase shift as a function of frequency.

You can estimate frequency-response models and visualize the responses on a Bode plot, which shows the amplitude change and the phase shift as a function of the sinusoid frequency.

For a discrete-time system sampled with a time interval T, the transfer function G(z) relates the Z-transforms of the input U(z) and output Y(z):


The frequency-response is the value of the transfer function, G(z), evaluated on the unit circle (z = expiwT) for a vector of frequencies, w. H(z) represents the noise transfer function, and E(z) is the Z-transform of the additive disturbance e(t) with variance λ. The values of G are stored in the ResponseData property of the idfrd object. The noise spectrum is stored in the SpectrumData property.

Where, the noise spectrum is defined as:


A MIMO frequency-response model contains frequency-responses corresponding to each input-output pair in the system. For example, for a two-input, two-output model:


Where, Gij is the transfer function between the ith output and the jth input. H1(z) and H2(z) represent the noise transfer functions for the two outputs. E1(z) and E2(z) are the Z-transforms of the additive disturbances, e1(t) and e2(t), at the two model outputs, respectively.

Similar expressions apply for continuous-time frequency response. The equations are represented in Laplace domain. For more details, see the idfrd reference page.

Related Examples

More About