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Module « scipy.signal »

Fonction residuez - module scipy.signal

Signature de la fonction residuez

def residuez(b, a, tol=0.001, rtype='avg') 

Description

help(scipy.signal.residuez)

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

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

             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

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

See Notes of `residue` for details about the algorithm.

Parameters
----------
b : array_like
    Numerator polynomial coefficients.
a : array_like
    Denominator polynomial coefficients.
tol : float, optional
    The tolerance for two roots to be considered equal in terms of
    the distance between them. Default is 1e-3. See `unique_roots`
    for further details.
rtype : {'avg', 'min', 'max'}, optional
    Method for computing a root to represent a group of identical roots.
    Default is 'avg'. See `unique_roots` for further details.

Returns
-------
r : ndarray
    Residues corresponding to the poles. For repeated poles, the residues
    are ordered to correspond to ascending by power fractions.
p : ndarray
    Poles ordered by magnitude in ascending order.
k : ndarray
    Coefficients of the direct polynomial term.

See Also
--------
invresz, residue, unique_roots

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