Module « scipy.signal »

Fonction residuez - module scipy.signal

Signature de la fonction residuez

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

Description

residuez.__doc__

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