This is documentation for an old release of SciPy (version 0.10.0). Read this page Search for this page in the documentation of the latest stable release (version 1.15.1).

scipy.signal.invres

scipy.signal.invres(r, p, k, tol=0.001, rtype='avg')

Compute b(s) and a(s) from partial fraction expansion: r,p,k

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

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

H(s) = —— = ———————————————-

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

See also

residue, poly, polyval, unique_roots