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# 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

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