invres#
- scipy.signal.invres(r, p, k, tol=0.001, rtype='avg')[source]#
- 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:
- rarray_like
- Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions. 
- parray_like
- Poles. Equal poles must be adjacent. 
- karray_like
- Coefficients of the direct polynomial term. 
- 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:
- bndarray
- Numerator polynomial coefficients. 
- andarray
- Denominator polynomial coefficients. 
 
 - See also