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