Mathematics

Partial Fraction Expansion

residue finds the partial fraction expansion of the ratio of two polynomials. This is particularly useful for applications that represent systems in transfer function form. For polynomials b and a, if there are no multiple roots,

where r is a column vector of residues, p is a column vector of pole locations, and k is a row vector of direct terms. Consider the transfer function

b = [-4 8];
a = [1 6 8];
[r,p,k] = residue(b,a)

r =
   -12
     8

p =
    -4
    -2

k =
     []

Given three input arguments (r, p, and k), residue converts back to polynomial form.

[b2,a2] = residue(r,p,k)

b2 =
    -4     8
a2 =
     1     6     8

Polynomial Curve Fitting

Interpolation