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 - residuefor 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_rootsfor further details.
- rtype{‘avg’, ‘min’, ‘max’}, optional
- Method for computing a root to represent a group of identical roots. Default is ‘avg’. See - unique_rootsfor 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