scipy.signal.residue

scipy.signal.residue(b, a, tol=0.001, rtype='avg')

Compute partial-fraction expansion of b(s) / a(s).

If M = len(b) and N = len(a)

b(s) b[0] s**(M-1) + b[1] s**(M-2) + ... + b[M-1]

H(s) = —— = ———————————————-

a(s) a[0] s**(N-1) + a[1] s**(N-2) + ... + a[N-1]

r[0] r[1] r[-1]

= ——– + ——– + ... + ——— + k(s)

(s-p[0]) (s-p[1]) (s-p[-1])

If there are any repeated roots (closer than tol), then the partial fraction expansion has terms like

r[i] r[i+1] r[i+n-1]

——– + ———– + ... + ———– (s-p[i]) (s-p[i])**2 (s-p[i])**n

Returns:

r : ndarray

Residues

p : ndarray

Poles

k : ndarray

Coefficients of the direct polynomial term.

See also

invres, poly, polyval, unique_roots