scipy.signal.residuez#
- scipy.signal.residuez(b, a, tol=0.001, rtype='avg')[source]#
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
- barray_like
Numerator polynomial coefficients.
- aarray_like
Denominator polynomial coefficients.
- tolfloat, 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
- rndarray
Residues corresponding to the poles. For repeated poles, the residues are ordered to correspond to ascending by power fractions.
- pndarray
Poles ordered by magnitude in ascending order.
- kndarray
Coefficients of the direct polynomial term.
See also