scipy.signal.residue¶
- scipy.signal.residue(b, a, tol=0.001, rtype='avg')[source]¶
Compute partial-fraction expansion of b(s) / a(s).
If M = len(b) and N = len(a), then the partial-fraction expansion H(s) is defined as:
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 together than tol), then H(s) 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