Function Reference
— Function File: [r, p, k, e] = residue (b, a)

Compute the partial fraction expansion for the quotient of the polynomials, b and a.

where M is the number of poles (the length of the r, p, and e), the k vector is a polynomial of order N-1 representing the direct contribution, and the e vector specifies the multiplicity of the mth residue's pole.

For example,

          b = [1, 1, 1];
          a = [1, -5, 8, -4];
          [r, p, k, e] = residue (b, a);
                r = [-2; 7; 3]
                p = [2; 2; 1]
                k = [](0x0)
                e = [1; 2; 1]

which represents the following partial fraction expansion — Function File: [b, a] = residue (r, p, k)
— Function File: [b, a] = residue (r, p, k, e)

Compute the reconstituted quotient of polynomials, b(s)/a(s), from the partial fraction expansion; represented by the residues, poles, and a direct polynomial specified by r, p and k, and the pole multiplicity e.

If the multiplicity, e, is not explicitly specified the multiplicity is determined by the script mpoles.m.

For example,

          r = [-2; 7; 3];
          p = [2; 2; 1];
          k = [1, 0];
          [b, a] = residue (r, p, k);
                b = [1, -5, 9, -3, 1]
                a = [1, -5, 8, -4]
          
          where mpoles.m is used to determine e = [1; 2; 1]

Alternatively the multiplicity may be defined explicitly, for example,

          r = [7; 3; -2];
          p = [2; 1; 2];
          k = [1, 0];
          e = [2; 1; 1];
          [b, a] = residue (r, p, k, e);
                b = [1, -5, 9, -3, 1]
                a = [1, -5, 8, -4]

which represents the following partial fraction expansion