invresz(r, p, k, tol=0.001, rtype='avg')
If :None:None:`M`
is the degree of numerator b
and :None:None:`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 :None:None:`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 invres
.
Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions.
Poles. Equal poles must be adjacent.
Coefficients of the direct polynomial term.
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.
Method for computing a root to represent a group of identical roots. Default is 'avg'. See unique_roots
for further details.
Compute b(z) and a(z) from partial fraction expansion.
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._signaltools.residuez
scipy.signal._signaltools.invres
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