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# 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`

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