System Identification Toolbox™

tfdata - Numerator and denominator of transfer function from idmodel object

Syntax

[num,den] = tfdata(m)
[num,den,sdnum,sdden] = tfdata(m)
[num,den,sdnum,sdden] = tfdata(m,'v')

Description

m is a model given as any idmodel object with ny output channels and nu input channels.

num is a cell array of dimension ny-by-nu. num{ky,ku} (note the curly brackets) contains the numerator of the transfer function from input ku to output ky. This numerator is a row vector whose interpretation is described below.

Similarly, den is an ny-by-nu cell array of the denominators.

sdnum and sdden have the same formats as num and den. They contain the standard deviations of the numerator and denominator coefficients.

If m is a SISO model, adding an extra input argument 'v' (for vector) will return num and den as vectors rather than cell arrays.

The formats of num and den are the same as those used by the Signal Processing Toolbox™ and Control System Toolbox™ products, both for continuous-time and discrete-time models.

The noise input channels in m are treated as follows: Consider a model m with both measured input channels u (nu channels) and noise channels e (ny channels) with covariance matrix

where L is a lower triangular matrix. Note that m.NoiseVariance = . The model can also be described with a unit variance, normalized noise source v:

• tfdata(m) returns the transfer function G.

• tfdata(m('n')) returns the transfer function H (ny inputs and ny outputs).

• If m is a time series, that is, nu = 0, tfdata(m) returns the transfer function H.

• tfdata(noisecnv(m)) returns the transfer function [G H] (nu+ny inputs and ny outputs).

• tfdata(noisecnv(m,'norm')) returns the transfer function [G HL] (nu+ny inputs and ny outputs).

Examples

For a continuous-time model,

num = [1 2]
den = [1 3 0]

corresponds to the transfer function

For a discrete-time model,

num = [2 4 0]
den = [1 2 3 5]

corresponds to the transfer function

which is the same as

Note that for discrete-time models, idpoly and polydata have a different interpretation of the numerator vector, in case it does not have the same length as the denominator vector. To avoid confusion, fill out with zeros to make numerator and denominator vectors the same length. Do this with tfdata.

See Also

tf

timestamp