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Module « scipy.signal »

Fonction invres - module scipy.signal

Signature de la fonction invres

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

Description

help(scipy.signal.invres)

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

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