scipy.signal.residuez

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

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

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

        b(z)     b[0] + b[1] z**(-1) + ... + b[M-1] z**(-M+1)
H(z) = ------ = ----------------------------------------------
        a(z)     a[0] + a[1] z**(-1) + ... + a[N-1] z**(-N+1)

         r[0]                   r[-1]
 = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ...
   (1-p[0]z**(-1))         (1-p[-1]z**(-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]
-------------- + ------------------ + ... + ------------------
(1-p[i]z**(-1))  (1-p[i]z**(-1))**2         (1-p[i]z**(-1))**n

See also

invresz, poly, polyval, unique_roots