scipy.signal.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_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
- bndarray
Numerator polynomial coefficients.
- andarray
Denominator polynomial coefficients.
See also