# scipy.signal.residuez¶

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

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

If M is the degree of numerator b and N the degree of denominator a:

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


then the partial-fraction expansion H(z) is defined as:

        r                   r[-1]
= --------------- + ... + ---------------- + k + kz**(-1) ...
(1-pz**(-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


This function is used for polynomials in negative powers of z, such as digital filters in DSP. For positive powers, use residue.

Parameters
barray_like

Numerator polynomial coefficients.

aarray_like

Denominator polynomial coefficients.

Returns
rndarray

Residues.

pndarray

Poles.

kndarray

Coefficients of the direct polynomial term.

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