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