[r, p, k] = residue(b, a)
[b, a] = residue(r, p, k)
| Parameter | Description |
|---|---|
| b | vector: numerator polynomial coefficients. |
| a | vector: denominator polynomial coefficients. |
| r | column vector: residues. |
| p | column vector: poles. |
| k | row vector: direct term (empty when the rational function is proper). |
| Parameter | Description |
|---|---|
| r | column vector: residues. |
| p | column vector: poles. |
| k | row vector: direct term. |
residue computes the partial fraction expansion of the ratio of two polynomials b(s) / a(s).
With two inputs, it returns the residues r, the poles p and the direct term k such that
b(s) / a(s) = r(1) / (s - p(1)) + ... + r(n) / (s - p(n)) + k(s).
For a pole of multiplicity m repeated in p, the corresponding terms are r(j) / (s - p) ^ 1, ..., r(j + m - 1) / (s - p) ^ m.
With three inputs, residue performs the reverse operation and returns the numerator b and the denominator a of the equivalent rational function.
[r, p, k] = residue([1 0], [1 -3 2])[r, p, k] = residue([2 5 3 6], [1 6 11 6]);
[b, a] = residue(r, p, k)