Navigation

Operators and Keywords

Function List:

C++ API

: [num, den] = padecoef (T)
: [num, den] = padecoef (T, N)

Compute the Nth-order Padé approximant of the continuous-time delay T in transfer function form.

The Padé approximant of exp (-sT) is defined by the following equation 

             Pn(s)
exp (-sT) ~ -------
             Qn(s)

Where both Pn(s) and Qn(s) are Nth-order rational functions defined by the following expressions 

         N    (2N - k)!N!        k
Pn(s) = SUM --------------- (-sT)
        k=0 (2N)!k!(N - k)!

Qn(s) = Pn(-s)

The inputs T and N must be non-negative numeric scalars. If N is unspecified it defaults to 1.

The output row vectors num and den contain the numerator and denominator coefficients in descending powers of s. Both are Nth-order polynomials.

For example: 

t = 0.1;
n = 4;
[num, den] = padecoef (t, n)
⇒ num =

      1.0000e-04  -2.0000e-02   1.8000e+00  -8.4000e+01   1.6800e+03

⇒ den =

      1.0000e-04   2.0000e-02   1.8000e+00   8.4000e+01   1.6800e+03

Package: octave