Module « scipy.signal »

Fonction invres - module scipy.signal

Signature de la fonction invres

def invres(r, p, k, tol=0.001, rtype='avg') 

Description

invres.__doc__

Compute b(s) and a(s) from partial fraction expansion.

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

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

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

               r[0]       r[1]             r[-1]
           = -------- + -------- + ... + --------- + k(s)
             (s-p[0])   (s-p[1])         (s-p[-1])

    If there are any repeated roots (closer together than `tol`), then H(s)
    has terms like::

          r[i]      r[i+1]              r[i+n-1]
        -------- + ----------- + ... + -----------
        (s-p[i])  (s-p[i])**2          (s-p[i])**n

    This function is used for polynomials in positive powers of s or z,
    such as analog filters or digital filters in controls engineering.  For
    negative powers of z (typical for digital filters in DSP), use `invresz`.

    Parameters
    ----------
    r : array_like
        Residues corresponding to the poles. For repeated poles, the residues
        must be ordered to correspond to ascending by power fractions.
    p : array_like
        Poles. Equal poles must be adjacent.
    k : array_like
        Coefficients of the direct polynomial term.
    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
    -------
    b : ndarray
        Numerator polynomial coefficients.
    a : ndarray
        Denominator polynomial coefficients.

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