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5.7  Parametric transfer function

Except for the id_poly and qbode functions, the SDT does not typically use the numerous variants of the ARMAX model that are traditional in system identification applications and lead to the ratio of polynomials called transfer function format (tf) in other MATLAB Toolboxes. In modal analysis, transfer functions refer to the functions characterizing the relation between inputs and outputs. The tf format thus corresponds to the parametric representations of sets of transfer functions in the form of a ratio of polynomials

    Hj(s) = 
aj,1 sna−1 + aj,2 sna−2 + … + aj,na
bj,1  snb−1 + bj,2 snb−2 + … + bj,nb
    (5.27)

The SDT stacks the different numerator and denominator polynomials as rows of numerator and denominator matrices

    num = [
a11a12        … 
a21a22… 
 ⋱ 
]  and   den = [
b11b12… 
b21b22  … 
 ⋱ 
]     (5.28)

Other MATLAB toolboxes typically only accept a single common denominator (den is a single row). This form is also accepted by qbode which is used to predict FRFs at a number of frequencies in the non-parametric xf format).

The id_poly function identifies polynomial representations of sets of test functions and res2tf provides a transformation between the pole/residue and polynomial representations of transfer functions.


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